Wombats are protected under the NSW Biodiversity Conservation Act 2016. It is an offence to harm a wombat unless a licence is obtained from the Department of Planning, Industry and Environment.30 July 2019

Wombat stew is definitely not allowed.

I've only seen snow once and I've only seen a wombat in the wild once, trudging purposefully through that snow. A memorable day.

Having said that - from my environmentally friendly Aussie soap box - I think the children's book version of the song is the more likely answer for your song search because it would be better known, I think.

And as it happens, the wombat and his friends outsmart the dingo who was trying to make
Wombat Stew

"One day, on the banks of a billabong, a very clever dingo caught a wombat ... and decided to make... Wombat stew, Wombat stew, Gooey, brewy, Yummy, chewy, Wombat stew! In this classic Australian picture book, a dingo catches a wombat and wants to cook him in a stew. But all the other bush animals have a plan to save their friend. They trick the dingo into using mud, feathers, flies, bugs and gumnuts in his stew, and the result is something the dingo will never forget!"