When it first started, Doctor Who was on for nearly ten months a year. The regulars got the odd week off here and there with their characters being written out of particular episodes in various ways.
Sometimes they would just appear in pre-filmed sequences; other times a stand-in would double for them in long shots; in one particular story, the Doctor was made invisible (apart from his hands) and all his dialogue was pre-recorded while somebody else played the part of his hands!
The companions were sometimes captured and locked up in cells for an episode which meant that they didn't appear. They used all sorts of ingenious ways to write them out for a week or two in those days.
To go back to the original question, I say let's see a few episodes with DT before we start wondering when he's going! If Christopher Eccleston's departure hadn't been so quick and well publicised, I'm sure people wouldn't be wondering this.