OP, it's lovely that your DD likes animals, especially dogs. You've had lots of good advice already on the practicalities and issue to think about if you take on your own dog.
I just wondered if you had thought of the many ways that you can get more "hands on" time with dogs and build up your DD's interest/awareness - either as a prelude to dog ownership or quite possibly as an alternative.
Many rescues offer the opportunity to sponsor a dog - these are an ideal birthday present for children. Sponsors get regular updates, photos, info, magazines etc, and in some rescues can even go and meet the dog concerned.
Also many rescues offer lots and lots of great fun, (and very inexpensive) events that are ideal for families. Just thinking about some of the ones round here, there are regular tea parties (with home made cake
) where you can go along and meet/make a fuss of some of the dogs, regular walks, quizzes, BBQs, taster events, and of course wonderful charity dog shows. At this time of the year, practically every weekend there is a little rescue show somewhere - classes never cost more than a £1 to enter, and they are great fun to attend, with lovely stalls and a great atmosphere. Again you can meet and get to know lots of lovely dogs. We regularly go with our nephew to some of the local events, and now he often gets asked to take foster dogs into the ring and has a lovely time.
Some dog training clubs have children/junior handler classes - could be worth researching? Also, most rescues are desperate for regular dog walkers. How about you and DD making a regular commitment to a weekly walk? This would also be good for you to see how she reacts to this commitment and see if the novelty wears off, without the commitment of a full time dog of your own.
It's difficult to suggest specific rescues without knowing where you are but Google will help you.
Good luck 