Ed Joyce top-scored with 35 from 60 balls, sharing a third-wicket partnership of 55 with Niall O'Brien.
Queensland are 137-5 in reply, with one further day's play to come on Tuesday.
The fixture was arranged as preparation for Ireland's Intercontinental Cup game against Papua New Guinea, which begins in Townsville on Sunday.
Ireland currently top the Intercontinental Cup table with maximum points from convincing wins in their matches against the UAE and Namibia.
Openers William Porterfield and Paul Stirling were both dismissed cheaply, making only five, but the experienced pairing of Joyce and O'Brien led a fightback.
Joyce plundered four fours and a six in his innings, while O'Brien struck four boundaries in a fluent 26.
O'Brien's dismissal by Australian international Ben Cutting sparked a collapse in the Irish ranks, as Joyce followed shortly after.
Gary Wilson and Stuart Poynter both made 18, with Andrew Balbirnie (0) and Stuart Thompson (4) falling in quick succession to leave Ireland reeling on 122 for 8, with Clontarf professional Mick Granger (2-53) accounting for Wilson and Thompson.
Tim Murtagh made a solid 20 before he was dismissed by Andy McBrine (1-14) - both the Donemana all-rounder and George Dockrell were playing for the hosts.
Indeed it was Dockrell (1-5) who brought the Irish innings to a close on 155 as he bowled Boyd Rankin for nine.
Craig Young took an early wicket but a second wicket stand of 68 between Scott Henry (50) and Nick Stevens (33) put Queensland firmly in the ascendancy.
Young came back to break the partnership, having Stevens well caught by Stirling.
Former Australian Under-19 international Sam Truloff (9) became Boyd Rankin's (1-15) first wicket back in Irish colours as Ireland rallied late in the day.
Stuart Thompson had Henry caught behind by O'Brien, before Stirling bowled Scott Bazley with the last ball of the day as Queensland finished 18 runs adrift.
Ireland's batsmen showed signs of rustiness as they were dismissed for 155 on the first day of their game against a Queensland XI in Brisbane.