[ghostguy6]

Personally It pains me to say this as I firmly believe you should be allowed to hunt with any firearm that you can shoot accurately.

I would not go hunting with a Gsg 16 ( or any tactical looking rifle) at this point. Given the political climate towards firearms even being seen with a "scary gun" could hurt legal gun owners. If you make a mistake and end up in the media your .22 plinking rifle will be turned into an " Evil weapon of mass destruction capable of killing hundreds of school children" Even the Ruger 1022 is a better option but even that one seems like it will be on the chopping block sooner than later.
If I were to purchase a new firearm for rabbit hunting right now it would be a bolt action .22 that would accept both flush mounted and higher capacity magazines with a wooden stock. I would use the shorter magazines for hunting if on public lands. Plus being that it is not a semi automatic it will likely be legal longer.
You seem relatively new to shooting so a bolt action will help you learn the fundamentals of proper shot placement. Plus it can save you a little money when it comes to ammo.