Is it possible for a bathroom countertop to be held up by angle brackets
Given a 6' wide slab, brackets are the right choice. In my ideal world, there would be at least 2 from the back wall, equally spaced, as well as ledgers on the sides. Be sure the brackets and ledgers are well attached to studs. 

Stone/quartz/etc will often have plywood underneath to support the slab. Talk to your vendor about who is providing it, if it's necessary. If it's you, ask what thickness they want. (This-all assumes a built-up nosing.)

Lots of possibilities for brackets, but if you can't find anything locally, google 'fastcap speedbrace'.