Some do yes, but it's not very common. It's sold in supermarkets though. after WW2 rabbits helped feed peoole In a country where there's wasn't a lot to go around. It's not so prevalent these days.
My operations out on that farm aren't hunting though, it's culling, and none of what I shoot leaves the farm unless it's a deer. It's actually illigal to shoot kangaroos and take the meat without government issued tags. Of course, that doesn't go for rabbits which are an intruduced pest species that government would dearly love to totally eradicate.
I've eaten rabbit now and then although it's not something I'd want to live on if there were other options.