obtain her Thai passport from the appropriate Thai consulate or the embassy, whichever serves where u live. when here, obtain her national ID and drivers license if she's old enough for the latter. The Thai passport alo offers visa free travel to other Asian countries.
I just applied for the LTR and received a response asking for my health insurance. Despite the fact that the application has a box to check that says it can be submitted later (which I checked).
Also I have Blue Cross Blue Shield health ins which covers me worldwide but what I have from them may not satisfy the BOI.