We get on when you get off - take good care of her for us!
So there is a Budget that is quite close. Depending on your desire to walk, you could definitely walk it. Assuming there is more than one of you, one person could get the car and the other person could wait with bags. There are some covered benches over by the design center (the giant white building across from the terminal). And the Budget is right near the Silver Line to the airport (which frankly would probably be faster, easier, and cheaper than trying to do a one at rental to the airport, but obviously depends on your plans).
Here is the info for the Budget: