I want to make a reservation with my points as a "seat holder" for my child. (She will have my Companion Pass, once I earn it later this month.) Can I buy a ticket for a minor without an unaccompanied minor fee?
If I am following you correctly, you want to use points for a minor who will ultimatley be travelling with you on a future flight as a companion (for free using CP). Is that correct?
If that is the case, to accomplish what you are talking about, you would use points to purchase a ticket for the minor. As part of the purchase process, the SW system online will ask you to enter your information and link your reservation to the minor's (therefore, he/she will not be unaccompanied).
Once your CP comes through, you can cancel the points purchase (the points will refund to your account, and the taxes can be re-used for the traveler) and then add the minor as your companion on the trip.
I will say that you cannot be 100% sure that "holding" the seat now will absolutely guarantee that you will be able to add them as the companion later. In theory, you can cancel the points purchase, and even if the flight is sold out, it should free up a seat to grab with CP. With that said, there are booking scenarios where that might not be able to happen. I think it would be rare, but it is a thought.
I hope I have understood your question and that this helps!
-A List Preferred, Companion Pass holder, Community Champion.