There is a tune (not a song, but maybe you can make words to it) called 'ferret panting' on Damien O'Kane and Shona Kipling's CD 'Box On'. They might still have it on their myspace.
If a hamster will do instead of a ferret, you can find Ed Pickford's song about 'Hamster Sid' on his youtube or songbook site.
And if a rat or mouse is an acceptable substitute, let me know and I will look up a Doc Watson song about a rodent that gets drunk...