The National League side came from a goal down to beat AFC Wimbledon 3-1, who lost defender Paul Robinson to a red card after taking down Sutton striker Matt Tubbs.
Sutton have also beaten Cheltenham Town, Dartford and Forest Green Rovers on their way to the fourth round.
Now Doswell is looking ahead to a big meeting against Garry Monk's in-form Leeds team, who are likely to rotate against the non-league side.
And the Sutton boss insisted his players would not be fazed in the televised encounter, which will take place on Sunday, January 29 (kick-off 2pm).
"Without being over-emotional about it, we have got a good chance against Leeds on our pitch," Doswell said after the Wimbledon victory.
"No one likes playing on it apart from us it seems. We are very good on it.
Sutton have won 12 of their 16 matches at Gander Green Lane this season and held League One side Wimbledon to a goalless draw in the original third round tie.
Doswell made it clear to Monk that he cannot afford to see this fixture as a rest for his top players.
"No disrespect to Leeds but if they make seven or eight changes against us I think we will have a chance,” Doswell added.