Charlie Hemphrey (48 not out) and Sam Heazlett (37 not out) are the unbeaten batsmen for Queensland.
Earlier in the day, keeper-batsman Matthew Wade brought up a century for Tasmania before being dismissed for 108, while Sam Rainbird (57) became the fifth player for the innings to reach 50 for Tasmania.
Queensland fast bowler Brendan Doggett finished with figures of 5-101, while Michael Neser claimed two wickets as Tasmania were dismissed in the 139th over.
Queensland reached 1-128 at tea, with Matthew Renshaw the first man out for 37.
Joe Burns (49) and Marnus Labuschagne (32) also got starts for Queensland, with Tom Rogers claiming two wickets for Tasmania.
Play will begin at 9am tomorrow.
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