Rovers’ Centre of Excellence side recorded the stand-out result of the second round when they thrashed the current cup holders 5-0 at their Cobham training ground.
Derby County, who booked their place in the last eight with a narrow 2-1 victory over Birmingham City at St. George’s Park, will host the quarter-final tie on Saturday March 2nd.
Rovers' Under-17 head coach Matt Johnson said: "It’s an exciting draw and one that we will need to play well in again to progress through to the semi-finals.”
The draw, which was made in La Manga by England Women’s manager Hope Powell, sees Rovers’ fledgling female stars follow in the footsteps of their male counterparts, who visit Derby County in the fourth round of the FA Cup this weekend.
Quarter-final draw in full:
Everton v Colchester
Derby County v Rovers
Oxford v Aston Villa
Lincoln v Arsenal