Gluing to stained wood?

So this is a sort of a combination of topics… I’ll explain.

I’m making a toy box for my nephew and the faces are birch plywood, I’m planning to give it a dark red stain. I’ve also cut some Celtic knot designs out of oak (won’t be stained) and want to attach them to the sides/front. I’ve never actually done any finishing before so I really don’t want to screw this up… will there be an issue gluing my oak designs to the birch after it’s been stained or is that a no-no? I’ve thought about putting some screws in from the inside of the box into the design but the design is pretty thin and I’m not sure that’s the best method. Any suggestions on how I should approach this? I can provide pictures if that would make it easier to see what i’m trying to do.