I started out the same as you a few years ago, still on the lookout for places myself..
It will have to be private property with owners permission to use an air gun for hunting.
occasionally I'll head to my bosses lifestyle block for a walk but more often than not when I do see bunnies they're out of Air rifle range or already running,
its a start but you'll probably want to upgrade to something with more reach and power if looking at public land.
A good air rifle is a nice tool to have for learning the fundamentals and using on small properties where you want to ensure shots don't leave the boundaries.
I use a .22cal Gamo Maxim paired with H&N Hornet pellets when hunting.
I can usually hit within a 30mm circle at 50meters (not as accurate as my rimfire rifles but it does the job)
At 24 joules (1.05 gram pellets at about 700fps) its got enough power to kill rabbits and hares but shot placement is key.
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