The Tigers reached 5-257 at stumps on day one of the Shield season after George Bailey won the toss and opted to bat under grey skies on what looked to be a menacingly green wicket on Tuesday.
But, in a rematch of last year's Shield final, the visitors handled it with early aplomb to cruise to 1-188 before a late Bulls fightback - including a collapse of 3-7 - restored the balance.
Former Test No.3 Doolan (115) looked typically untroubled in reaching his 10th first class century, slaying anything short through point and dispatching a Mitchell Swepson full toss to the square leg boundary to bring up triple figures late in the second session.
"We were keen to take on the challenge of batting first here and hopefully tomorrow it quickens up and our bowlers can do a bit of damage," the four-Test player told AAP.
The 32-year-old said continuing Tasmania's resurgence, rather than pushing for another chance at the highest level, would drive him this season.
"I don't think about it at all," he said of his chances of a Test berth this summer.
"I think that ship's probably sailed for me and if someone gets caught up in thinking about Test spots, who's in and who's out, it just takes away from your own game.
"Tassie's come a long way in the last 12 months, 18 months, to challenge for silverware in almost every competition we play."
A patient 43 from Beau Webster, who shared in a 134-run stand for the second wicket with Doolan, helped Tasmania into a commanding position after a slightly delayed start due to rain.
But Queensland's patience was rewarded late in the day, with Peter George (3-42) finding the centurion's edge and Luke Feldman (1-49 off 26 overs) toiling hard.
Former Test gloveman Matthew Wade was unbeaten on 37 at stumps and will be key to their push for a 350-plus total on Wednesday.
Meanwhile, Queensland trio Matthew Renshaw, Michael Neser and Brendan Doggett will fly home after not being selected for the second Test in the United Arab Emirates, but will not be available until the second round of Shield action against South Australia in Adelaide.