Which got me wondering if I could find the lyrics to the songs I remembered.
Why, yes, yes I can.
OLD MAN EMU (John Williamson) http://lyricsplayground.com/alpha/songs/o/oldmanemu.shtml
Please Don't Call Me A Koala Bear (Don Spencer*) http://www.moron.nl/lyrics.php?id=83119&artist=Don%20Spencer
Where Does A Goanna Go? (Don Spencer) http://www.weeks.id.au/lyrics/don-spencer/where-does-a-goanna-go.php
Sugar Glider (Don Spencer) (not my favorite, but I DO remember it) http://www.weeks.id.au/lyrics/don-spencer/sugar-glider.php
* incidently, I think I remember the name 'Don Spencer' on the video tape, which might be a little odd since it included Old Man Emu
EDIT: Okay, looking at the index page (http://www.weeks.id.au/lyrics/) I have to admit to remembering all of them.