Welcome here! That’s nice of you to want to help your cousin, but I don’t think this is the solution.
Basic Training is for our military Jersey, I believe it’s several weeks… maybe 3 months long?
What is going to happen at the end of this, the bunny is going back home to her? I think the bun would be better off staying at home. Even with just getting food and basic care, the stress of a flight across the country and then back again is a lot for a relatively short time period. Someone would have to fly with the bunny (they cannot fly cargo), so there would be the additional cost of a person flying to and from 4 times.
Another (better) option would be to seek out a pet-sitter or boarder in Ohio for the few months. There are a couple HRS chapters in Ohio that have pet-sitting you can work out.
Western Ohio: http://www.ohare.org/
In the Columbus area: http://www.columbusrabbit.org/
Now even if she has to drive the bunny a couple hours to drop him off, it would be much better and less stressful than a flight.