He was hoping that things would work out well. The Doctor always tended to hope that things would work out well - his life would have been unbearably stressful if he didn't. Plus, a long lifespan spent traveling in both time and space had given him a certain perspective on hideous situations involving almost certain death. So far none of them had ended that badly.
Like all good youngsters on Gallifrey, the Doctor had been brought up with a strong awareness of how little other species new about... anything and how they usually shouldn't been told about, well... anything, because most of the information a Time Lord might be able to offer them would at least make them retire to the country and keep bees - should their planet have bees, or similar life forms - if not actually drive them irreversibly insane.
