Runner:
Doing your own research is fantastic! Most people here do, and as long as you stick to credible websites and information, you will learn a lot.
As for the surgery, I would imagine that your daughter has a hematologist and dentist or oral surgeon? The Hemo would manage the platelets and the dentist should manage antibiotics for any infections. Many times, the specialists (Hemos) will not prescribe for infections, so you should ask the dentist about that. If she does have an infection, I can't believe they would just ignore that. Maybe they will prescribe after the surgery.
Most cases of ITP in children are primary. It is unusual for a child to become diagnosed with another autoimmune disorder as the primary and ITP the secondary, especially a child as young as yours. I have seen a few adolescents develop Lupus which is then the primary disorder, but that is rare. Lupus and Thyroid problems are the top autoimmune disorders that can go along with ITP, but as I said, not normally in children that young. Many times, an autoimmune disorder such as Lupus cannot be diagnosed for years anyway since it can take a long time to develop. Tests probably won't help at this point. If she doesn't have any strange symptoms, I wouldn't worry about it. Without symptoms, it's hard to run tests if you don't know what you are looking for.
The main trigger for ITP in young children is vaccines, mostly the MMR. Sometimes an illness can trigger it, or an antibiotic. In those cases, there isn't much you can do but wait it out and hope that remission occurs.