Doidge's first goal was cancelled out by United substitute Adrian Sprole.
But the Premiership side progressed after Doidge, who has taken his tally for the season to 14, twice netted from Joe Newell corners.
Ross, who played down suggestions of Hibs being interested in Sunderland winger Aiden McGeady, said: "Christian has been terrific since I came to the club. His scoring return over two and a half months has been excellent.
"I believe he will continue to score regularly.
"If he does that he will end up with a very healthy total, more than justifying the decision to bring him to the club.
"I can't comment on anything prior to November but his all round play has been good, a great player to work with, terrific personality, very unselfish."
United manager Robbie Neilson reaffirmed United's determination to hold on to Shankland beyond the closure of Friday's transfer window.
Scouts from Sheffield United, Queens Park Rangers and Stoke City watched the 24-year-old notch his 27th goal of the season.
Neilson said: "I would have preferred if he'd saved that until just after January, when the window is shut.
"He showed his quality but he can still improve.
"We don't have to sell any players. We're financially stable, Lawrence is a major part of what we're doing here, he'll continue to be a part of that – and we'll reassess where we are in the summer."