The 33-year-old Briton finished eighth on the time-sheets in the first round of qualifying, with his new team-mate Sergio Perez fourth quickest as the overhauled car's lack of pace was offset by the sodden conditions at Albert Park circuit.
McLaren were 2.4 seconds off the pace in the Friday practice dominated by Red Bull in dry conditions, and Button suggested there would be nowhere to hide if the rain held off on Sunday when the final qualifying sessions will be held early before the late afternoon race.
"(The car) rides a little bit better and I think we've lucked into this weather a little bit," a frowning Button told reporters, hunched under an umbrella to shelter from the pouring rain.
"I think we were quicker in these conditions, not on the wet (tyre) but on the inter tyre and I think judging it right has made a big difference to us when we've put our lap-time in.
"It's going to be a tricky day tomorrow because it looks like its going to be sunny, but we'll do the best we can. The aim still has to be to pick up points."
Scattered showers are forecast on Sunday, but Melbourne's changeable weather could easily see the track turn bone-dry before final qualifying or the race.
After McLaren's underwhelming performance on Friday, last year's winner Button, who won a championship with Brawn GP in 2009, said McLaren would struggle to make the third round of qualifying.
Team principal Martin Whitmarsh said Friday's practice was one of the "hardest days" he could recall, and conceded the team had taken a risk making significant changes in the offseason to the car that won the final two races of last year's championship.
"My coffee stop and the beach is blown, but there you go," Button joked of the abridged qualifying.
"On a serious note, for the guys (in the garage) it's a lot more stressful for them ... It's going to be a busy busy day tomorrow but we've done it before and I think that their skills will come through tomorrow."
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