Pet rabbits seem so sweet.

They are less likely to cause problems with children/adults who are normally allergic to cats and other animals.

They are easy prey to three year olds though! Be careful about this.

They have no control over urine and feces and free roam will produce a mess in your house.

If you have a linoleum floor in your kitchen I would put up gates and let the bunny roam there, easy clean up. ( check out the link below lol! )

Check into the deworming formulas too.

Read about other people who have pet rabbits and get their advice. You can google it. I know my close friend has one in a cage in the kitchen, her and her kids are allergic to everything, but the rabbit has caused no problems. They play baby with it, wrap it in a blanket, and it lets them push it around in a toy baby stroller!
http://mfrost.typepad.com/cute_overload/bunnies/index.html

I feed my rabbit a raw diet. ..He's old, and living a lot longer than I thought he would (he's an inbred pure bred). He became much healthier after I switched him over to a raw diet. ..I feed him a base of grass hay and a little less alfalfa hay. Along with the hay, I feed apples, grapes, oranges, dandelion greens(1 of his favorites), swiss chard, squashes... Pretty much any kind of fruit or veggie I have on hand, everything's mostly organic... I wouldn't recommend lettuce though, it has pretty much No nutrition. ...I also feed my 2 guinea pigs a raw diet with NO guinea pig pellets, and they're very healthy. To keep my rabbit's (and all of my animals) parasites under control, I just put a couple drops of pure oregano oil in their water. ...I used to breed and show rabbits, so I've had a lot of experience with them. I wish I had known more about feeding a raw diet at that time, they live so much longer and are so much healthier, instead of feeding rabbit pellets. ...And regarding your 3 year old with a rabbit, it should be fine, as long as you're always there watching when your 3 year is petting/playing with the rabbit, & make sure he/she knows how to treat the rabbit. ...Rabbits do chew a lot, so you'd have to watch out for that when it's out(it could chew chords, depending on the rabbit). I haven't tried litter box training, but I've heard it can be done. ..What I've always done, is just let them out in the house for about an hour at a time to exercise. ..Some rabbits will become scared of people when they are left loose all the time.