You included the right answer in your question: GAP covers the difference between the vehicle's actual cash value (what her insurance pays you for the total loss) and the remaining balance on your loan. That's all GAP covers, in fact.
No you don't have to buy another Jag, in fact you don't have to buy anything at all. The other idiot's insurance pays just for your vehicle (depreciated retail value), your GAP policy covers whatever you still owe the lender, and you're back to Square One.
If you were a good customer, and it sounds like you were, that same lender will probably be happy to set up another vehicle loan.