Rangers edged a point clear at the top of the Sky Bet Championship but endured a frustrating evening in front of goal as the clash at Loftus Road ended goalless.
They had won their previous four matches 1-0 but could not even muster the solitary goal which would surely have seen off a Brighton side who are hardly prolific themselves.
And Redknapp revealed afterwards that Bobby Zamora will be out until after Christmas following a knee operation.
With Andy Johnson also sidelined, Charlie Austin was the lone frontman but he missed two good chances and was relieved to see an offside flag when he dragged a third wide from all of three yards.
R's boss Redknapp, who is monitoring Tottenham's Emmanuel Adebayor and Harry Kane, said: "I thought we did well as we've only got one striker.
"Bobby Zamora's had an operation and Andy Johnson is out so we are still short up front. I need more options really.
"We need someone. But what you find at this time of year is it's not easy to find someone decent.
"But we couldn't have worked any harder and defensively we look strong."
It was actually midfielder Joey Barton who looked most likely to break the deadlock.
He had the ball in the net after just eight minutes but Shaun Wright-Phillips was a long way offside when he crossed.
Barton forced a fine save from Tomasz Kuszczak with one curling free-kick and saw another bounce inches wide after taking a deflection which left the Seagulls keeper stranded.
Kuszczak was beaten when Matt Phillips nodded the ball over him during an almighty goalmouth scramble but Gordon Greer was on hand to hack the ball off the line.
Their final chance came on the stroke of full-time when Richard Dunne headed Barton's free-kick over the top.
Brighton showed little ambition with a couple of long-range efforts from Keith Andrews the closest they came.
Assistant boss Nathan Jones said: "We'd have loved to have taken all three points but let's not be greedy.
"They are a good side and not many teams will dominate them here, so if we are being honest as the away team a draw is a fair result.
"If you are a point behind QPR then you have a good chance of getting to the Premier League."