Arsene Wenger's side entertain Rovers on the back of a hard-fought win over Sunderland in which they had to survive the last 28 minutes with 10 men following the dismissal of Carl Jenkinson.
The Gunners held firm for a 1-0 win that moved them up to fifth in the Premier League and within touching distance of fourth-placed Tottenham, who they face in a fortnight.
But first up is the FA Cup clash at the Emirates and with spirits high in the Arsenal camp, Walcott is confident of progression.
"It was an important win," the forward told the official Arsenal website. "The three points have us on a high and we've got a nice week now without any midweek game.
"A lot of players are back from international duty and need a bit of a break. Some may be rested for the FA Cup game, but that's just as important as we want to go far in that competition.
"If we lost [at Sunderland], we would have been dwelling on it for so long, so I'm glad we didn't."
Walcott also feels his team have the strength of character needed to come through the challenges ahead and beat Tottenham to the final Champions League qualification place.
"We are very confident [of finishing in the top four]. We can battle through any sort of situation," he said.
"The teams around us are winning as well, but we have just got to make sure we look after ourselves and try to win as often as we can.
"We will see where we are at the end of the season, but we have got to show the belief we did at Sunderland. I felt there were a lot of winners in that dressing room and the boys were fantastic."