Having come through the youth system at Manchester United, the 21-year-old had two loan spells at the KC Stadium before making the move permanent in January.
Brady played an integral part in the Tigers' promotion back to the top flight and scored the decisive spot-kick as they picked up their first win against Norwich on Saturday.
The Ireland international followed that up with another goal on Tuesday, striking home moments after coming off the bench in extra-time to secure a 1-0 Capital One Cup second-round win at Leyton Orient.
Such performances come as no surprise to full-back Dudgeon - a fellow graduate of the Old Trafford youth system that also now plies his trade for Hull.
"Robbie is someone I have known for years now and the minute I saw him I knew he had something special," he said.
"If he gets his head down this year, he has the ability to be one of the best.
"If we can do well, he will shine and I am sure he will have a great career in football, be up there with the best in the league, the best in the country.
"I've got no doubts about that. He is a great player and a great lad. He deserves it."
Brady saved Hull's blushes in a game League One leaders Leyton Orient should have won.
Hull boss Steve Bruce made 11 changes for the match and few of the incoming squad players did themselves justice.
One highlight, though, was the performance of Dudgeon.
Having spent almost 11 months out with a knee injury, the 22-year-old looked decent and played the full 120 minutes.
"It has been a while," Dudgeon said. "It was a tough game and a good one to come back on, really.
"Fair play to them, they've got off to flier this season, so we knew it would be a tough game.
"It was a good 90 minutes for me and probably one of the better games. I got plenty of running in and plenty on the ball, so all-in-all a good game.
"It has been a long time. It was tough, but I am back now and hopefully shown I can be part of the team.
"It has been a long time and the lads were brilliant last year, so I am glad to be back in a team full of good lads and all my mates that helped me get through it. Hopefully I can move on from here."