Buy it on a PS3, link it in with your PSVita, then get it through Content Manager Assistant.
STEPS: (I don't really remember the process, but here are the things you have to do.)
1. Buy GT PSP on your PS3's PSN store (you must have the same SEN account as your Vita)
2. Wait for it to finish downloading
3. If it's finished, go press X on the GT PSP icon, then select "Transfer using Content Manager Assistant".
4. Download the game through your Vita by hooking it up with the PS3, select "PS3 to PSVita", find the selection "PSP/Other", then find GT PSP. You should copy it to the Vita.
5. After it's done copying, the game is installed. Enjoy playing GT PSP on the Vita.