While his title is director of football operations, he was only promoted last year when Reggie McKenzie was hired by the Raiders to become their GM, and he had been in charge of college scouting for the past decade. Obviously, that time period has featured a lot of great drafts. If the Packers do promote from within then Eliot Wolf might be the new right hand man for GM Ted Thompson but he's far from the most experienced candidate.
However, I could see them bringing in someone to replace Dorsey. The Packers have now seen three top executives depart for GM positions in recent years (Dorsey, McKenzie, and John Schneider in Seattle) and that's a lot of talent to lose. They might need to add an experienced someone from outside the organization to help them make up for all they've lost.