King Charles III and Queen Camilla will sample a traditional barbecue, along with more formal ceremonial engagements, when they visit Australia next month.

The trip will be the King’s biggest overseas since he began treatment for cancer in February.

Running from 18 to 26 October, it will include a review of the Australian naval fleet in Sydney harbour as well as meetings with political leaders and two award-winning cancer experts.

After the Australian leg of the trip, the King and Queen will travel to Samoa for the Commonwealth heads of government meeting.

The King is still receiving cancer treatment and the events will be paced to take account of his health. An accompanying visit to New Zealand has already been postponed on medical advice.

Since his diagnosis, the King’s only trip overseas has been to France for D-Day commemorations in June.

This Australian trip, the first of his reign to one of the Commonwealth realms where he is head of state, will be much more extensive and include a series of public engagements in Sydney and Canberra.

It could prompt further questions about the future of the monarchy in Australia and the debate about whether the country should move to become a republic.

On his arrival, the King will be officially welcomed by Australia’s Prime Minister Anthony Albanese.

Among the themes of the King’s trip include him hearing about the impact of climate change on the environment.

He will meet two award-winning experts in the treatment of melanoma, Georgina Long and Richard Scolyer, with Australia having one of the highest levels of skin cancer in the world.

At a barbecue near Sydney, the royal visitors will meet a diverse range of community representatives and local farmers.

The Queen, meanwhile, will visit projects about tackling domestic abuse and violence against women.

The Australia trip will be followed by the Commonwealth heads of government meeting in Samoa, which the King had seemed determined to attend for the first time.

The King has spent much of the summer in Scotland, including marking the second anniversary of the start of his reign this weekend.

There was more positive news about the King’s health last week, with royal sources saying he was “heading in a very positive trajectory”.

Queen Camilla also described the King as “doing very well” when she visited a hospital in Bath.