In the hardware store you can buy thick garden fencing in 1/2"x1/2" grid size. I've used it to make a litter box screen, but I think it would make good bunny fencing too. It's much thicker than chicken wire, which bunnies can bite through.
I would make the fence at least 3' high so that the bun can't jump out. I would also dig the fence into the ground a bit, or some fencing horizontal in the ground so the bun can't dig out at the edges. Using some wood to frame the edges would make it much sturdier too.
If the bunny will be out there without supervision, I would absolutely make a top for it too - it's so easy for a stray cat or hawk to get in there if you're not standing right next to it (or even your dog if she changes her mind about the bunny some day).
