Doogue fired over the winner in the 40th minute of the second-half with just 20 seconds remaining on the match clock. The winner capped a superb comeback for Laois, who trailed by 1-7 to 1-10 in the closing minutes, before sub Olywn Farrell netted and Doogue had the final say.
Meath forward Ger Doherty, the match winner in the semi-final victory over Dublin, came off the bench again and landed three points from play but sin-binnings for Meath’s Jenny Rispin and Louise McKeever cost them.
Laois got off to a dream start when Martha Kirwan netted after just 20 seconds to cap a flowing move involving Anna Moore and Mary Kirwan.
But scores from Gráinne Nulty (two) and Kate O’Brien had Meath level by the 11th minute and they moved ahead for the first time in the game when Elaine Duffy slammed home a 25th minute penalty.
Laois responded with points from Mary Kirwan and Tracey Lawlor, both frees, to restore parity by half-time, 1-4 apiece.
The sides were level on three further occasions during the second-half before Meath, who put together a scintillating run of five unanswered points, moved into a 1-10 to 1-7 lead.
With the clock running down, Meath looked good for victory but there were still a couple of late twists to come in this tale.
In the 37th minute of a stop-start and physical second-half, Doogue’s shot was saved by Irene Munnelly but Farrell picked up the pieces for a levelling goal.
And with extra-time looming, Doogue raced through to secure the Mary Ramsbottom Cup for the O’Moore County.
Scorers for Meath: E Duffy 1-2 (1-0 pen, 1f), G Doherty 0-3, K O’Brien 0-3 (2fs), G Nulty (0-2).
Scorers for Laois: T Lawlor 0-4 (3fs), Martha Kirwan, O Farrell 1-0 each, Martina Dunne 0-2, Mary Kirwan (f) and Sinead Doogue 0-1 each.
MEATH: I Munnelly; L McKeever, A Murray, O Sheridan; S Bennett, E Rahill, K Allen; K O’Brien, G Nulty; C O’Shaughnessy, E Duffy, F Mahon; J Rispin, M Sheridan, V McCormack.
Sub: G Doherty for Duffy (42).
LAOIS: C Dollard; L Hyland, G Dunne, E Healy; A Taylor, J Moore, M McEvoy; A Casey, T Lawlor; Mary Kirwan, A Moore, M Dunne; Martha Kirwan, S Doogue, G Weston.
Subs: O Farrell for Martha Kirwan (ht), D Callanan for M Dunne (50), A Quigley for Hyland (56).
Referee: P Kehoe (Carlow).