my daughters first pet

Fish are great for this age!! A small aquarium can be inexpensive and you can get a couple of gold fish. Have her help pick out the gravel and decorations for the tank to.

I know it is not something furry and cuddly, but it is a start with being responsible for a pet. And as a bonus the water fliter sounds at night tend to be soothing for kids!

Start her off with a stuffed animal. Seriously, you can't expect a 3 1/2 year old to actually take care of the pet.

Now, if you're asking what a good pet would be for you to take care of, but that she could also interact with (while supervised of course), then that's a whole different story.

Really, I'd have to recommend rats over hamsters. Rats are more friendly in general and have good balance so kids are less likely to drop them (but she'll need to be supervised and she'll need to be sitting down).

And by the way, any animal with teeth can bite. But if properly handled, rats are unlikely to bite her. However, the operative part here is that YOU must be supervising at all times to ensure she is properly handling the rat.

Honestly, from the way you worded your post it sounds like a stuffed animal would be best. Or maybe one of those cute robotic ones where the kid has to take care of it, but no living creature dies when they fail to do so.