I agree with Jasper, it's been done before; there are a lot of old trucks that only ever had a full wood flatbed. If I were going to go about doing this, I would end seal all boards with epoxy. Wood is like a straw; so to seal those ends, you can accomplish a lot in regards to stabilizing the bed. I would also epoxy any through bolt holes; as both the aforementioned areas, holes, and cut ends are where you'll get the most rot over time.
As far as the bed itself, I think oiling it, and maintaining a schedule for that, say yearly would be an intelligent move. In regards to strength, and holding up that camper, that's up to how you engineer the bed. I would consider 'burnishing' the support members, then oiling them; heck, if you burnished the sides of it enough, and oiled it, I think it would end up looking painted. I don't think I would paint any of the wood except maybe the edges for appearances.
Also, regarding the materials necessary for your endevour, I'd buy larch/doug fir; I don't think it really matters if it's kiln dried, or green, I think I'd rather have green for the cost savings, as kiln dried isn't going to help. The green will be easier to cut, and work with. Once dry, then you can oil, and seal, or what you choose. As far as fasteners, for structural components, I'd stay 3/8", and larger on bolts, and as far as screw fasteners, I'd go with stainless, or ceramic coated.
Another place you could save money, is instead of using doug fir/larch, for the actual bed, you maybe able to pick up some black cottanwood/poplar, which imho is the best decking material you can get. The would is **** to work with structurally, as it twists, but to nail down right over framing, when green, it'll lay nicely. The best part of the black cottonwood is, that it 'shreds' instead of chipping; so rather than anything heavy chipping it out, it'll 'shred', if that makes sense.