Kirk had no plan. Except to TRY SOMETHING! He does not believe in the no win scenario. He had also just been through McCoy's sedating him and pumping him full of other drugs.
Seemed perfectly in character to me. Has he ALWAYS had a plan? In every episode? Every incident? Every movie? 'Course not!
And where do people get this idea that the trip to Vulcan only took minutes. That wasn't clear in the film I saw. Kirk is sedated, and when he wakes up they're almost to Vulcan. Everyone else has changed clothes. We have no idea how long it's been. Coulda been hours. Doesn't matter!