They're changing how they treat Thai citizens who enter Thailand on a foreign passport now. So they will be seen as Thai rather than foreign nationals by immigration.
What that actually means, who knows as it's a recent change. Maybe no need for extensions or fines? But you can also just get a 12month extension at immigration for 1900B, just by proving her Thai citizenship (ID card, Passport etc.)
Depends on the airline, I've seen some people say they've been asked from Australia. But I haven't been in the last 2 years. That's with Thai Airways, Jetstar & Singapore Airways.
Look into onward flights, so if needed you can quickly buy a cheap ticket ($10-20) at the check-in counter.
Children (under 14 or 16?) can't be fined or banned for overstaying. So she can come and go.
You could also go to immigration and get a 1year extension for 1900B if you wanted. It would require her birth certificate and proof of your Thai citizenship (ID card, Passport etc.), or if she has Thai citizenship documents then they would also work.