The managerless Championship side carved out two excellent chances early on, Gavin Anderson sending a flashing header over from a Jamie Hamill cross from the right after two minutes and seconds later Dobbie surged forward and brought out a terrific save from Alloa goalkeeper Neil Parry.
Queens dominated with Parry batting away a fierce Dobbie drive after 25 minutes and one minute later Derek Lyle had a glancing header cleared off the line by Andy Graham.
In cup competitions the Dumfries side have been in imperious form and when the Doonhamers finally broke the deadlock in 41 minutes it was a strike of pure genius from Dobbie, who collected the ball 18 yards out and curled the ball high into the net. The League One side might have levelled two minutes later, but Greig Spence’s right foot 18-yard drive crashed off the far post.
Dobbie, who has been a revelation since returning north after a long spell in England, booked Queen of the South’s place in the last four when he headed in an Anderson cross at the back post in 76 minutes.