A pediatric dentist is a specialist that is absolutely necessary if she has any issues with her teeth.
Most family dentists did a round in pediatric dentistry during their college years but it's the same for those of us who had to take a general ed class requirement we weren't especially interested in. They know enough to think they can do anything but really don't have a lot of experience is dealing with baby teeth.
I think if she has a good check up that you could use your family dentist but I would not let them do ANY work on her, not even fillings. They just don't know.
I have a friend who decided to not take her daughter to our pediatric dentist and she took her to the family dentist. She had a cavity right in front. He filled it, it fell out, he filled it again, it fell out, he filled it a third time and then just told mom it couldn't be saved and he pulled the baby tooth. She is 8 and just this year the hole got a tooth. She was nearly 3 years without a front tooth. That's just sad.
Our little one fell at her moms on a concrete staircase. She broke off her front tooth and we took her to a kids dentist, Ocean Dental, and they took one look and said no way would they even touch her mouth. They gave us a list of pediatric dentists and I made the appointment. He took good care of her tooth, put her to sleep in an outpatient center at Children's hospital. She woke up and wanted to go eat and play.
Her cap was white, the tooth never fell out and had to be redone, it was still perfect when she lost it. I could not even tell which was the cap without looking very very closely.
That is the comparison between a regular family dentist and a pediatric dentist. I always take them to the pediatric one.
As for a pediatrician vs a regular doc...I am not that worried about the issues. If the child is sick a lot or has some developmental issues then I would only use the pediatrician. We had a DO that I loved, he was on the ball when it cam e to any issues with the adults but as for the kids, he didn't even know they could start eating rice cereal before 10 months old. I showed him the WIC vouchers and he was totally surprised. He wasn't a dad yet so maybe that was something most young guys learns as they raise one of their own.