I'm assuming you're talking single speed, right? QR with a single speed is totally doable. You need to make sure that your axle is not protruding past the edges of the dropouts. In other words, when you have the wheel in place, there should be extra space in the dropout. The skewer needs to be really tight, and that space is necessary, as the QR compresses the whole system.
Chain tensioners are for running single speed with vertical dropouts, when you can't adjust chain tension with the wheel position in the dropouts.