Normally the domicile of a minor child follows that of the parents - or of the custodial parent, if the parents are separated.
The VBTA law of 2018 - which gives the spouses of active-duty military the option of filing taxes under either their own domicile state or that of their servicemember spouse - does not mention children, but I suspect the minor child of the servicemember would have the same option as the civilian spouse, if the child had to file their own tax return. (But I haven't been able to find an internet reference that supports that opinion.)
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
