McGoldrick and Town captain Luke Chambers both headed home from corners in the first half to expose some flimsy defending.
McGoldrick, easily the most outstanding player on show, virtually ensured the result with his second on 51 minutes as Ipswich's unbeaten run was extended to six games.
A lifeless Doncaster, whose injury worries were obvious in some of their haphazard defending, have now won just once in 12 league games.
There was very little for those inside a half-empty Keepmoat Stadium to be enthused about in a bitty opening 20 minutes.
Neither side seemed determined to hold onto the ball for any period of time with Ipswich's holding midfielder Col Skuse ably mopping up the many stray passes on show.
Ipswich gave some notion of their aerial threat on 16 minutes when McGoldrick rose highest to meet a Ryan Tunnicliffe cross from the left but his header lacked any power.
It proved a sighter for Town's top marksman as he picked his spot when allowed a free jump at Aaron Cresswell's 24th-minute corner.
With the burly presence of Daryl Murphy attracting the attention of one too many defender, McGoldrick popped up in front to power home.
With Ipswich's second corner of the match six minutes later, they were 2-0 up.
The flag-kick was well won when McGoldrick's clever back-heel completed a one-two with Tunnicliffe and his pull-back was turned behind.
Tunnicliffe drifted the resultant corner across the six-yard box where Chambers, completely unmarked, needed only to make contact to score.
The ease of the goal drew howls from the home fans, although Rovers would have pulled a goal back before the break but for Dean Gerken.
The Ipswich goalkeeper made good ground to push a 25-yard Mark Duffy free-kick, headed for the top corner, onto the crossbar.
Ipswich earned a third corner just before half-time, but when Tunnicliffe opted to play it short - and the move quickly dissolved - he earned an earful from his manager Mick McCarthy for not testing a clear home weakness.
McCarthy's temper was never threatened again, however, as his side bossed proceedings after half-time against worryingly dispirited hosts.
McGoldrick deservedly grabbed his second on 51 minutes when again he had far too much space in a dangerous position to slide home after Murphy's low centre.
Murphy was denied a goal by Ross Turnbull moments later when through one-on-one with Frank Nouble's follow up offside.
Turnbull got down well to prevent McGoldrick's hat-trick as Doncaster's resistance went limp.
When the hosts did get in behind skipper Richie Wellens chose the wrong option, passing across goal when he could have shot at an exposed Gerken.
McGoldrick missed two more chances for his hat-trick, but when he was replaced on 83 minutes the travelling support had long already been singing his name.
Chambers almost completed a memorable Boxing Day for the Town fans when he burst into the area but flashed a shot wide in the closing moments.