Hi Wingfeet,
The nitrogen cicle will take weeks to establish, 2-3 weeks, 3 weeks more often. With first an ammonia spike and a nitrite spike which are very harmful to your fish, you have to wait with introducing fish till after those spikes occur.
Adding water of an established will tank will do nothing, due to the fact that the bacteria live in the filter, substrate and decoration such as rocks or otherwise.
What you can do is squeeze the filter media of a friend, and all the muck what comes with it in a plastic bag with aquarium water and then pour it into your filter, this way beneficial bacteria of the established filter will be introduced in your system.
Don't forget that bacteria need decomposing fish food or fish waste to grow, so it is good idea to use some fish food in your aquarium in small amounts, this way ammonia will build up in your tank, and the nitrogen cycle works better.
When introducing fish, do it gradually, don't buy a lot of fish at the beginning, because the biological filter, your bacteria may not be able to adapt to a large bioload that brings with it, so gradually increase your fish population.
Good luck with your new tank.
Regards,
Tercio