Can you please advise us what exactly is the booking class for your daughter's ticket on SQ? SQ does sell some cheap fares from the US to Australia via Singapore but as far as I know, these are restricted to the fares that do not earn miles unless something has changed recently.

There are many SQ fares that do not earn miles and this same non-earning booking class will extend to other FFP's as well.

The biggest issue on Krisflyer is that the miles earned on this programme expire within a certain number of years (4, I think) if you don't use them.

It is OK to earn miles on UA for example, I don't think you have much to worry about. There are many more people who have millions of miles in their account and I am sure they will be fighting for you to keep UA Mileage Plus alive if anything should happen.