Green’s Dictionary of Slang

(Aus.) absolutely contentedly, perfectly happily.

1941		Baker Popular Dict. Aus. Sl. 56: Like a possum up a gumtree, completely happy, in the best of spirits and contentment.
1945		Baker Aus. Lang. 87: Here are a few more similes snatched from our environment: [...] like a possum up a gum-tree (the gum-tree is the only Australian part of this phrase).
1955		N. Pulliam I Travelled a Lonely Land (1957) 235/2: like a possum up a gum tree – completely happy.
1964		E. Wier Rumptydoolers 21: Smellin’ her own lamb’s jacket makes her feel like a possum up a gum tree, real happy like.
1997		E. Fuller Emu in the Sky 179: ‘Remember when I told you about all those mystical revelations I had at the watering hole, ...’ ‘Ya was like a possum up a gum tree awright’.

in difficulties.

1821

R. Waln Hermit in Philadelphis (2 ser.) 24: ‘Up a slim pine, by Jupiter’ — ‘Up a gum-tree, by Jove’ — ‘Lord! just saved my bacon’.

(Aus.) excl. of irritation.

1919

Teed Dly (Murwillumbah, NSW) 17 May 7/4: And strike me up a gumtree, all his bloomin goods would bring / Wouldn’t buy the bottle diamond in a knuckle-duster ring.