My 3 1/2 year old plays with her "nookbook" which is the Nook Color. She plays on the drawing apps and angry birds and a few others I loaded up, and has her "read to me" books she gets to and "reads". She uses it more than I do, really.
I would wait and find out for sure what apps are available on the Fire and what if any they cost.
And make sure nothing on there is linked to your credit card