Move from 3/6 to 6/12?

[fluff]

The rake is $3 per round, about $12 per hour? In other words if it is a typical 9-10 handed game, the rake is around 30-33 cents per hand?

That game is SUPER BEATABLE. Instead of moving up, learn to beat this game first. If you can't bet this easy game (rake is only 1/10th of what a B&M game with standard rake rules), I doubt moving up will help.