Thanks Don and Harry! I will proceed with fitting a screen into the door. BTW, the door handle on mine is not working well. Have either of you replaced yours, and if so, was it tough to find that size? I'm having no luck finding a handle that small.
By door handle, do you mean the non-locking lockset (the knob below the deadbolt)? By "small" do you mean the diameter of the knob, the thickness of the door, or the offset from the edge of the door frame, or the length of the knob shaft, or...?
I haven't replaced mine, but I went to look at it, and it looks like it was replaced at some point. It seems a little loose. If I can't tighten it, I may have to shim it with a piece of 1/8" plywood cut to the diameter of the trim piece. My door is only 1-1/4" thick, which is probably too thin for a regular household lock set. The knob is about 2" in diameter and I'd say it could be bigger with no problem.
I think you'll have better luck searching at RV parts stores than say Home Depot - seems like they should have hardware scaled down for camper construction. Also, there are a lot of RV salvage places, and I'd guess they'd have a large selection of used ones, and you could check all the important dimensions over the phone.
Edit: BTW, the brand name on both the deadbolt and knob set is Weiser. A search on "weiser locks" or "weiser lock parts" may turn up what you need.