For now, either go to the store or order online and API master freshwater test kit, the new tank that you are planning to get, and also Seachem Prime. You will NEED these things no question or else your fish will likely die. In the meantime, water change water change water change!!! Do a 75% change every day, or 2 30% water changes a day if the 75% is to much work. Because you don't have the API test kit yet, there is no super accurate way of knowing your ammonia level so your just going to have to act like its high (Because it likely is). Even though it might be convincing to get strips because they're easy and cheep... they are inaccurate and in a situation like this a single part off might mean life or death for your fish. Once the API test kit, the new tank, and prime come in or you have bought them. At this point, add the gravel and décor from your old tank, fill up the tank with dechlorinated water, make sure the temp is right, then add in your fish. Next, watch this video on a fish-in-cycle. The guy in the video might be a bit strange but all of the info he's saying is good. Follow the video until you are seeing the results he explains in the video, then you will have a cycled tank for your fish. Also, whatever you do, don't change out the filter on the new tank. It holds all of the good bacteria that keeps your fish alive. Once your tank is cycled, you can make a better filter that helps keep that cycle (Or you can just do it from the beginning if you want). If you have any more questions please ask.
Here's the video on the fish-in-cycle:
Here's the video on making a good filter that holds the cycle:
I hope all of this info will help you to get a new tank and cycle it. Best wishes, Nele.