When imagining a door made out of a thin sheet of plywood, "warp" is the first thought that comes to mind.
An unsupported piece of plywood that allows one side more access to moisture than the other, will.
But, that is not the way it ends up when used as a door for a teardrop!
Since the door will be hinged, one edge is supported.
A piano type hinge is best for plywood because of the continuous support it provides.
If you install a window, it will also "stiffen" the broad expanse of "flat ".
The latch or lock will provide some stiffening on the opposite side, but only at one point.
A three point latch will solve the problem, but it gets pretty complicated for a simple door.
A better solution is to use a 1 x 2 or something similar, to create a stiffener that runs vertically near the latch edge.
Generally, using 3/4" or thicker plywood will greatly reduce the chances of the door ever warping, and pretty much negates the need for a brace.
A pre made door is okay too, if you can find the size and shape that compliment your profile, as opposed to just jamming whatever you can find in there.
Overall looks and symmetry aside, the larger the door, the more comfortable it is to use.