Full sized bed frame and head board.. could a queen mattress work?

You would have to widen the bed frame. The headboard would be too narrow but if you don’t mind that, then it could work.

This is what you need. Adapting the headboard is just a matter of doing something visual and creative. It could be a simple as hanging a curtain behind the headboard to make it appear wider to compensate for the additional width of the queen size mattress.

I wouldn’t do it.

Without complete support, the edges of the mattress edges will extend out over the bed frame. There would be an overlap, which would make it easier to fall out of bed and probably be hard on the mattress. Try it and if it doesn’t work, get just a queen mattress support. and sell your headboard or keep it for later in your life.

There are constantly ads for free Queen size bed frames and box springs (THE most popular size) being given away on Craigslist by people who don’t want the bother of lugging it with them when they
move.

Everytime Ive moved Ive taken my mattress (because I can roll it up) and given away or left the frame and box spring and picked up one from CL at my destination.

They’re particularly plentiful in the spring. Nowadays, however, with the recent upswing in bedbug reports, I’d also invest in a detection kit just to be sure.

I’d sell or get rid of the full frame and set up the new box spring and mattress on the floor temporarily, until you can find a frame, head board, foot board, for the new queen set.
Better than risking damaging the new bed and the hassle of trying to modify the smaller frame.
Yes, Craigslist is a great place to buy bed frames.