Can I "just" concrete over the existing gravel in this carport?
Two things about an exterior concrete slab.


Proper drainage. Pitch the slab slightly so the water drains away. 1/2" to 1" for 10' of run should be enough since it is covered. 
Proper compaction. Make sure the material under the slab is properly compacted. If you believe it needs more sand or gravel for better drainage or to level the area, then that added material has to be compacted before placing the concrete. Sand or road-gravel compacts better than loose stone. Undisturbed gravel with compacted sand for extra drainage or leveling would work great. Top soil makes a poor base since living matter can be compressed, so it is removed and made up with road-gravel or sand. Since you have a base that is not top soil and has been compacted by cars and settled for years you don't have that problem.


You have a well thought out design.

Good luck!