A miniature of the ship Sirius was until recently displayed in the Woden office block of the same name, occupied by the Department of Health.

HMS Sirius sailed under the command of Captain John Hunter, and set out with the First Fleet from Portsmouth, England, in 1787 to set up the first British colony in NSW.

The ship carried Captain Arthur Phillip, the first governor of NSW. It was wrecked on a reef near Norfolk Island in 1790.

The timing of the removal fuelled speculation it was connected to Australia Day.

But a Department of Health spokeswoman assured the Canberra Times that was not the case.

"The Department of Health has been working with the School of Artillery Puckapunyal at the Department of Defence on an arrangement to loan the Sirius Model Ship to the School," the spokeswoman said.

"The School of Artillery is currently undertaking restoration action on various HMS Sirius's artefacts and the intention is that this be used as part of a display for the next 12 months. The model has been moved from our foyer in preparation for transport and loan to Defence for 12 months."

Debate on whether the date of Australia Day should be changed divided the nation ahead of January 26.

Pink paint was dumped on a statue of Captain James Cook's head at St Kilda on Thursday, with the words "no pride" painted beneath his feet, along with the Aboriginal flag, AAP reported.

A bluestone monument near Melbourne zoo commemorating Burke and Wills was vandalised with green paint and the word "stolen" written on it.

Federal Health Minister Greg Hunt last week told media the government was "committed" to Australia Day.

He said opponents of the national holiday were from the "radical left" and they were at odds with the rest of Australia.

"Australia Day is about celebrating one of the world's most successful nations. A nation which brings together people from around the world. It's about the strength of who we are," Mr Hunt said.