I framed mine by putting two studs a foot apart and put two pieces of 2x6 horizontal at the right heights. The only reason I used 2x6 instead of 2x4 is because that is the material I had on hand. That stud spacing worked because I made my door extra wide to get a wheelbarrow in, so I had to...
I agree you are better off framing it. I'd be concerned that the plywood would warp if you don't. Something solid to hold the hinges is something else to consider. You could use nuts and bolts through the plywood if you want but screws are easier to put in or take out and redo if you get it...