Perhaps up the staircase, to the summit, then back down via Eskdale Spur, car would be at Mountain Ck.
Could go as follows:
[list=]
Night 1 Bivouac Hut, Staircase Spur
Night 2:Michel (check spelling?) Hut, Eskdale Spur
Night 3: Return to Vehicle
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If you made good time, and weather, driving conditions for the trip etc favoured you- it might be feasible to make Cleve Cole Hut, visiting the summit on the way. It's a popular thing for the "first day" if conditions are good, and you started your walk form Mountain Ck in the morning, as opposed to driving up from say, Melbourne that same morning.
On the second day you could visit nearby Howman's Falls, then head out via Eskdale Spur camping in the vicinity of Michel-check-spelling Hut.
Third day- walk back to the car.
It's not summer- but you know that. daylight is short, weather can be wild at any time of year- more chance in May than earlier in the year- but I've been there even in June- and had three straight days of clear skies with foggy starts. Don't base your kit on weather in the lowlands the day before you leave.
Have a great trip.
Cheers
WildLight