After Qxd2 white moves Qf6. What would you do?

I would lose, right.
So what about Te7 and if 2. Qf6 then Qg5

Te7 is not that strong, actually your main idea was fine. You just have to look for a correct answer to Qf6 :)

Sorry, no clue right now.

Don't worry, you can try again later <3