On the plus side, 4E characters tend to be more durable -- higher hit points, healing surges, and lower monster damage.
That being said, I think it requires the same adjustments that prior editions required. You tailor the game to the character, you reduce the amount of combat (and scale it), you might introduce henchmen, sidekicks, or hirelings. You can also, however, freely break "game balance" because there is only you and the one PC. Give them more powers, let them pick powers from any class, let them take feats regardless of tier, whatever.
I think solo campaigns are simultaneously the trickiest and most liberating type of campaign to run, as a DM.