Unless you learn your partner in fact was at high risk (injection drug use, gay/bi, ex-prisoner, immigrant from an HIV
endemic country), you really don't need testing
at all. But if your anxieties demand knowing your test is negative, a single test at 6 weeks is fine.
Congratulations on starting Gardasil. In the long run, that's a more effective health prevention step for you than worrying about HIV from this event.