Queensland declared on 240-9 in Brisbane, in reply to Ireland's first innings of 155.
Ireland opener William Porterfield and Niall O'Brien put on 56 for the second wicket before both retired.
However, the Irish lost five wickets for 26 runs and were 83-6 when the teams shook hands with a session left.
Gary Wilson hit 16 and Andrew Balbirnie nine but Stuart Thompson, Stuart Poynter and Ed Joyce all failed to score.
Ireland trio George Dockrell, Max Sorensen and Andrew McBrine played for Queensland, with the latter scoring an unbeaten 49.
Ireland move on to Townsville to face Papua New Guinea, with the third-round encounter starting on Sunday.
The Netherlands top the Intercontinental Cup table with Ireland six points behind in second.
Ireland struggled to a draw with a Queensland XI in a two-day practice game ahead of their Intercontinental Cup match against Papua New Guinea.