Corivar can keep up with anyone holding a torch, as he can create smoke at his location as a Standard action, and teleport to any smoke within 1000 ft as a Move action. Flying, he moves at 40 ft.
Personally, I think a little investigating back at the capital might give us some answers, and give us an opportunity to get some form of royal decree proving that we are, indeed, employed by the royal family. As is, if we just go chasing down the princess and her party, what reason would they have to believe that we have any legitimate reason for being there? We could be bandits trying to kidnap her for ransom for all they know, and for all we can prove.
As far as the lead they have, they are traveling by conventional means, which means that the party is certain to be able to catch up quickly, even after a detour.