Plucky Dagenham were overwhelmed after the first half, with Bournemouth only a goal to the good at the break through McQuoid's 30th-minute shot.
Daggers lost goalkeeper Chris Lewington, who was unable to come out for the second half after an early injury sustained in a clash with Matt Tubbs.
Bournemouth reject Jordan Seabright took over as Lewington's replacement and made several outstanding saves from Marc Pugh and Wes Fogden. But Seabright was finally beaten in the 59th minute by Pugh and then by a McQuoid volley 20 minutes later.
Bournemouth's new confidence since Eddie Howe returned as manager last month showed itself again with a fourth goal in the final minute.
Substitute Fogden rounded off a comfortable win with his first goal of the season in the last minute. Dagenham, who also lost Michael Spillane to injury, failed to trouble goalkeeper Shwan Jalal.