Thanks for all the replies!
All these suggestions are great! Though, I have to say that we've had a ferret, white mice, gerbil, guiena pig, cats, dogs, and hamsters over the years.
The ferret... nasty little thing, would hide under the couch and bite my ankles when I sat down. Nobody else experienced that hateful things "playing". The guinea pig was ok til it got loose. Those things are horrid to catch!
On the subject of rats, snakes, and lizards. My mother will refuse to visit me with these... and I'm scared of snakes anyways. Rats, uhm... that was a funny one because we were at a pet shop and there was this "giant" one. My daughter squealed in the store and ran off. So I think the rat is a no so far.
One of the things is that I have alot of time on my hands. So, it's not a problem for that kind of pet. I tend to play with the hamsters alot during the day when they wake up for whatever reasons.
I was also worried about having a small furry animal around my daughter due to the fragile nature of most of them. But, she's done remarkably well with the hamsters and we have only lost one in the past 2 years. That was a unfortunate accident tho and partially my fault. But the danged thing loved the recliner and that's where she'd run to all the time.
Bunny? Those things?
Sure... I just got the response of "Those things hurt when they scratch you!"
Why do I have such a picky child?