The dog that gained international fame by guarding a penguin colony on an island off Victoria's south-west coast has died, and there are plans afoot to erect a statue in her honour.

Oddball the fluffy, snow-white Maremma dog died last week at the age of 15 – or 105 in dog years.

"Old Oddball has gone to the big chook run in the sky and will rest in peace," the Middle Island Maremma Project posted to Facebook on Wednesday.

About 150 metres offshore from Warrnambool and connected at low tide, Middle Island is home to band of little penguins. Unfortunately marauding foxes had cut the island's population to fewer than 10 birds in 2005.