The hosts dominated before the break and should have been a goal or two up by half-time, before a more even second half of fewer chances.
Town hit the woodwork twice and had three penalty claims rejected, while QPR mastered just a single shot on target.
Ipswich first hit the post after just eight minutes when Danny Haynes sprinted past Fitz Hall and drove firmly against the near post.
Lee Camp parried a firm Jason De Vos header from an Alan Quinn corner before both sides could have scored in the space of 30 seconds.
First, Hogan Ephraim fired wide from Rowan Vine's pull-back, before Town broke and Haynes' goalbound shot was cleared by Damion Stewart.
Camp pulled off a stunning low save to deny Haynes, before Alan Lee appeared to be flattened by Michael Mancienne, but referee Paul Armstrong rejected the penalty claim.
Town could still have scored as the loose ball dropped to Gavin Williams but he fired over.
The dangerous Haynes was pushed wide in the second half and Ipswich lost a lot of their threat as a result.
Lee floated a header over from a Quinn cross, before Patrick Agyemang glanced a near-post header wide at the other end.
Sub Martin Rowlands finally produced Rangers first on-target shot 64 minutes in, but Stephen Bywater saved easily.
Camp produced another fine save to palm away a 25-yard Quinn curling free-kick as Ipswich pressed for a winner.
They came agonisingly close again six minutes from time when Owen Garvan's effort flicked off Mancienne against his own post and Town claimed a penalty for handball as Matthew Connolly cleared Velice Sumulikoski's follow-up, but they had to settle for a draw.