How can I obtain a child dependent visa for my daughter born in Thailand?

The fact she's born in thailand as a foreign child doesn't matter at all 😕

AND

no matter what passport control tells you there is no overstay fine for children under 15 and no overstay banning for children under 18. They can't deny the child entry NOR can it cause you any issue as a parent of a foreign child on overstay. I know foreigners here who have children on multi-year overstays who exit/re-enter without any issues.

Your employer is a little confused as far as how the process works.

Your child can CAN get a 90 day Non-O visa based on being the family member of a foreigner who legally works here issued inside the country at the immigration office where you get your extension done for 2000baht.

The child cannot be on overstay when you apply, AND they need a minimum of 15 days left on their current free stamp entry because the application goes under review for 2 weeks before you go back to get the Non-O visa and new 90 day stamp inked in

Once that 90 days runs down you would apply for a yearly extension of stay that matches your employment extension stamp for 1900baht at the immigration office. Then every year when you get your new extension you get a matching extension for the dependent child