When you say parakeets are on the forbidden list does that mean you can't bring them into the state when moving? I'm in Casper and our local Petco sales ParakeetsWyoming like all states has import regulations for bringing in any live animals which includes your pet dogs and cats, livestock and poultry. Other than the import regulations, I am not aware of any state regulations against poultry.
Individual cities may or may not allow poultry in urban areas. Typically there are limits to how many hens may be allowed and also no roosters. Non urban areas may have zoning requirements that prohibit having any animals that can be considered food. Some HOAs may also have covenants against poultry. You will have to check the specific zoning and covenants or municipal ordinances for the site you choose.
One of the oddities of Wyoming is that parakeets are on the forbidden list.