I need to build a custom door for a bathroom in an RV. The door will be about 71" tall by 25" wide. What I would like to do is to take a 1/4" sheet of sanded plywood as the main body of the door and then place 1x4 Pine all the way around the edges on both sides plus a diagonal piece across on both sides. I would use pocket screws to join the 1x4s together at the corners.
Will this be strong enough to not sag? I am trying to reduce the weight as much as possible while still being no more than 1.75" thick to accept a standard door knob.