Sorry to be so long in responding. I've been using the classic production of a live rabbit in my empty top hat to close my family and children's shows for over 30+ years (not the same rabbit of course). IMO the only way to do it is as described; i.e., don't use stupid boxes or other props that no one will believe are empty, etc. -- just a top hat which you introduce in its collapsed state, then "pop" open, show clearly empty and produce the rabbit. In my personal routine, after showing the hat empty, I produce an egg, 6 colorful silks and a can of pork and beans from the hat, then show the hat empty again just before the rabbit appears in the hat when the kids say the "magic word."
I've found that the ONLY suitable breed of rabbit to use is the "Netherlands Dwarf." They only grow to 2 1/4 - 2 1/2 pounds (the perfect size for the top hat), are easy to train and care for, friendly, calm, gentle and like to be petted. Typical lifespan is 6-7 years although I had one that lived to 9. In my experience, the females seem to be a bit more docile than the males, but I have used both with no problems for over 30 years.
One important note: be sure that the rabbit is "empty" before you take it to the show(s) -- i.e., give it food and water when you get home after the show(s).
Hope this helps.