The specific Australian ad involved lamb and there is a tradition of offering a lamb's head to Ganesha.
According to Fact and Theory in Social Science (1964) at pages 213-214:
Still later in the winter comes Magh Cauth. ... A figure of a lamb , made of sugar , is brought to the sanctified place . When the moon is rising , the younger brother of the father of the boy , or a Brahman , sacrifices the lamb by decapitating it with a knife and offers the head to Ganesh.
This same text is repeated in Anthropology in the Development Process (1977).
Similarly, Culture and Mental Health
Cross-cultural Studies · Volume 10 (1959) at page 285 says:
Magh Cauth or “ Magh fourth , ” as the name suggests , is observed on the fourth day of the dark half of the month of Magh. ... When the moon is rising , the lamb is " sacrificed ” by decapitation with a knife . Some families ask a Brahman to do this , but the more usual thing is to have the father ' s younger brother act in this capacity . The head is lifted up and offered to Ganesh...
According to Nepal, Land of Gods, Goddesses, and Demons (1985):
Unlike in India , where Ganesh is a scrupulously vegetarian god , in Nepal , he is considered blood - thirsty , living near burning ghats and the abodes of evil spirits . So animal sacrifices are made to him regularly .
The book A South Indian Subcaste: Social Organization and Religion of the Pramalai Kallar (alternative link) lists Ganesh in the table on page 396 under both "vegetarian" gods and "meat eater" gods, vegetarian based upon what should be offered to Ganesh in principle, but meat-eater based upon what is offered to Ganesh in fact.
Overall, there is no consensus on whether or not Ganesh is vegetarian.