First up, sorry to hear about your dogs being attacked and one being killed. That shouldn't happen and there are laws to prevent this. Every state has a dog act, which lists the laws relating to dogs. These laws apply in the country just like in the city. There are no exceptions.
Dogs must remain on their property at all times. It doesn't matter if you live in the city or the country, they must remain on their property at all times. The only exception is if they are on a lead in a public place with someone who is holding the lead and capable or controlling the dog. The other exception is a designated dog exercise area, which allows dogs to be let off the lead in a public place. However, those dogs must still remain under control and be within a reasonable distance of their owner.
Dogs must be under the control of their owners whenever they are not on their property.
Dogs must not attack people, other animals or livestock. Dogs that do attack other animals and livestock are considered wild/ feral dogs and can be shot if they are on your property threatening you, or your pets/ livestock.
If a dog threatens you or someone on your property or in a public place, you are allowed to defend yourself with whatever force is deemed necessary to prevent injury to you or those being threatened.
As an elderly person, if a large dog comes onto your property and threatens you or your pets, and the dogs have already done this and killed one of your pets, you are fully entitled to defend yourself by shooting the aggressive animal and taking the owner to court for injuries or damages sustained during the attack. This is assuming you have a fire arms license and a legally obtained fire arm that is registered with the relevant authorities.
Even if you don't own a fire arm or a license for fire arms, you are still allowed to defend yourself with whatever force you deem necessary to protect yourself and your pets/ livestock.
Now if you were a 20 year old male that was 6 foot tall and built like Arnold Schwarzenegger, and a chihuahua came up and barked at you, and you kicked or hit or bashed that dog, it would be excessive force and you would be charged with animal cruelty.
But as an elderly person being threatened by two large dogs, that have already killed one of your pets on your property, most people would say you can use whatever means you see fit to protect yourself. If that means using an unregistered fire arm or a cross bow or even an axe to defend yourself from a large breed of dog that has come onto your property and is threatening you or your pets, that would be considered acceptable force in the eyes of the law.
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If the local Police/ Sherriff won't get involved, the council should because the dog act is normally enforced by local government (council).
All dog attacks should be reportedly immediately and if a pet is injured or killed by another dog, the council or cops have the right to seize the offending animal and have it destroyed if it's considered dangerous.
Your Sherriff and council can both be involved in this matter, as can animal control. But it needs to be dealt with by them. You need to file a complaint with the council rangers, animal control and the Police/ Sherriff and make sure they do something about this. If they don't, kick up a stink and write to state and federal governments and let them know, and contact the press.
If nobody will do anything, contact a civil lawyer and get them to investigate the matter.
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I have been attacked by over 50 dogs during my life, and I have had one of my dogs declared dangerous by a corrupt council who fabricated a dangerous dog declaration because I served the CEO of the council with legal papers over a council tree damaging my car.
Dogs that attack and kill other animals do not stop with just one attack. They continue attacking people and killing animals, be it pet dogs, birds, wild animals, etc. They do not change their behaviour and it takes a very responsible owner to retrain and control their dog/s after it has started killing. Your neighbours are not responsible owners because they let their dogs wander at large instead of keeping them confined to their own property.
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You have every right to be on your property and feel safe and not get attacked, threatened or molested by anybody's pet that is roaming the streets unattended. Likewise your pets have every right to be on your property and not be threatened, attacked or killed by uncontrolled animals that are roaming the streets and coming onto your property uninvited.
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Keep written notes including the day, date and time the animals come onto your property, where they went on your property, and what they do on your property.
eg: Thursday 17 December 2020, 11:17am.
Two large dogs came onto my property and walked up to my front door. One of them urinated on my door and the other crapped on my lawn. Both dogs wandered around my front lawn for approximately 5 minutes before leaving my property.
I was on my front lawn when they first came onto my property and I went inside when they came towards me, or came onto my property.
One dog was light brown and had short pointed ears that stood up.
The second dog was primarily black with a white patch on its side. This dog had big floppy ears.
Neither dog was wearing a collar, or the brown dog had a red collar and the black dog might have had a collar, I couldn't tell.
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Get photographs and video of the dogs every time they come onto your property. Include date & time stamp on the pictures if the camera has this feature. This will give the authorities positive identification of the dogs and prove they are coming onto your land. And if you have a date/ time stamp on the picture, it provides that information too.
Include some pictures and video showing a larger area around the dogs to prove that there are no people anywhere near the dogs. But also get pictures and video of the dogs so they fill up the picture frame to give clear positive identification of the animals.
If you can, get a motion sensor camera and set it up on your property. This will photograph or record video of anything that triggers the motion sensor. If you get video of the dogs coming onto your property, that is enough to force the council to act. If you get video of the dog/s threatening you or your pets, that is enough to have the animals declared dangerous and potential destroyed.
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Have you reported the death of your Dachshund to the Police/ Sherriff and council?
If not, then do it. And if you have a vet report for that incident and the other dog that was injured, send a copy of those reports to those departments.
Keep pestering the relevant authorities until they do something about this. You should not feel threatened, intimidated or concerned about strange dogs coming onto your property and harming you or your pets.