Could you schedule an additional appointment at the psychiatrist's office to take it so it doesn't infringe on your 1 hour time?

I don't think the MMPI is available online, at least not the official MMPI. It would compromise the results of the test, I think. I know that tests similar to the Big Five personality test are readily available online. The Big Five measures openness, agreeableness, extroversion, conscientiousness, and neuroticism. You could take that and bring it to your T, since it measures some similar traits.

You can actually take one here at Psych Central, by clicking "quizzes" on the navigation bar, then clicking Psych Central's Personality Test. It's the first one under the personality category.