Aside from the reasons cited by Cecil for the name not being associated with GP, it is unlikely that macho soldiers and motor pool mechanics would risk the usage of the (perhaps somewhat effeminate) “Jeepie” in nick-naming their vehicles.
Link to the “classic” column from 2000: Origin of “jeep”
Welcome to the Straight Dope Message Boards, Narce, glad to have you here and an interesting comment! When you start a thread, it’s helpful to other readers to provide a link to the column in question. Yeah, it’s on the home page now, but in a few days it will sink into the massive archives; so, providing a link saves searching time and helps keep us all on the same page. No biggie, you’ll know for next time, and, as I say, welcome indeed!