Several states require that a vehicle that comes from the factory w/ doors must have them on when you drive. The catch is that since the jeep doors come off so easily you could argue that they aren t installed by the factory and are designed to be a part that is optional to the owner. The biggest problem you will have though is if the mirrors are attached to the door, as you must at least have a driver s side mirror. If it is attached to the door (most likely) you will be out of luck, legally. Some jeep owners purchase a bracket and attach a mirror to the frame to get around this, but with the rental that isn t an option.
When you rent something, you cannot make those kinds of modifications. If you do, they ll most likely charge you a huge fee to repair the jeep. I suppose you could get away with it if you can return it with them back on with no evidence that they were ever removed. Why not try to rent a vehicle that already has the specs you want?
Probably not---the rental contracts are very specific---especially if you alter the vehicle. Also, there are lots of limitations with the rental companies on taking vehicles off road