I'm afraid I'm not much help here, because I'm on the fence on this issue. On the one hand, I think if you raise a child up with an animal, they will learn the respect and love that is due to animals. But this requires so much supervision...ie, you really can't leave the baby and animal alone together becasue both are so unpredictable. Just an example, I watched my five year old niece, who is a total tree hugger animal lover at her tender age, punch my dog on the side tonight. Not in malice, but because the dog is so playful and friendly that the niece is basically viewing Glory as a large and animated toy. In this situation, I don't blame either dog or kid (though of course I corrected the kid) and fortunately Glory has such a sweet personality, she didn't even blink.
Cats are less predictable than dogs, IMO. Speaking of nieces, Sissy did get them a cat because they wanted one and then propmptly had him declawed

mad: ) because in play he would scratch the kids. Dogs, especially if you get the right breed, are much more trainable than cats but again, when both (kid and dog) are young, constant supervision is highly recommended. In the case of getting a kitten, accidents are less likely to happen, because cats will simply dissapear from a situation they don't like, whereas dogs will continue to hang around.
We had one cat prior to Em's arrival, so we had to adapt no matter what. The second cat adopted us when Em was about three, but then again he is my sweet baby Stewart, so he wouldn't harm a fly. Glory we got right after Em turned 5, and they have had some issues (puppy nipping) but all is well.
Sorry if that was less than helpful...bottom line is, if you really want a pet for Lizzy at this age, I think a cat is the way to go.