How do you mount a dryer with no wall studs?

[#1]

For a Gyprock wall there will be timber or metal studs unless the Gyprock is glued directly onto masonry. If these don't line up with where you want to position the dryer brackets, cut a piece of timber (for example, 90 x 35 pine) that is long enough to span two or more studs or even across the room corner to corner.

Fix the timber firmly with construction adhesive and screw into the studs at the height you want then fix the dryer mounting brackets to the timber. Don't attempt to use Gyprock-only fixings. - martin1

The only suitable option is to bridge the gap between studs with timber. You should find the studs spaced 450mm apart and potentially in the corners if it is a tiny room. If you haven't already tried one, I'd suggest investing in a stud finder. - MitchellMc