A Pentax K7 fits what your asking. It's about as small as an aspc DSLR can be.
Get an extra battery or 2.
The camera and kit lens(18-55) is weather proof. It also does acceptable HD video.
A reasonably priced WR 50-200 is also available.

PS Keep the lens cap on when not in use. Blowing sand is hell on coatings and glass.