William Bronson wrote: The solid roofing will heat up from the sun and then radiate heat into the space beneath it.
If that space includes your rabbits, they will get hot as well.
To build an "attic" lay 2x4's across the horizontal parts of the carport frame and screw them to the tubing with long self tapping screws.
Attach insulative board, foil side up to the top of the 2x4s, with screws and fender washers.
Close in the open ends of the frame that form triangles with mesh to keep out wildlife but allow air flow.
Cap your roof with a ridge vent and you should have decent convection air flow through the attic.
Add a solar powered fan if you want but that might be overkill.
If you want to use the attic for drying/storing hay, screw your fan boards to the bottom of the 2x4s and plywood on the top and frame a hatch into the floor.
I would NOT put any of your own body weight into the attic floor, but it should hold hay just fine.