It was the first time the Queen had missed the CHOGM meeting in more than 40 years.
The Queen is the head of the Commonwealth but there are no provisions for it to be handed down to her successors. That will depend on agreement from the 54 countries which form the Commonwealth.
A report in the Australian says Gillard revealed in a recent speech that in early 2013 Geidt flew to Adelaide to seek her support for Prince Charles to be appointed the head of the Commonwealth group when Charles succeeded the Queen.
In her speech in London on the future of the Commonwealth, Gillard, a republican, said she had obliged with a request she make a clear statement by referring to Charles as the future head of the Commonwealth in Parliament.
"I would not want you to think this was some simple act of colonial subservience. I did see wisdom in it."
The campaigning shows the concern the Queen has about the future of the Commonwealth and calls in some quarters for an elected head to replace the monarch.
The Queen is head of state of 16 of the 154 Commonwealth countries and there is speculation countries such as Australia and New Zealand will become republics once the Queen's reign ends.
Leaders can expect another gentle nudge at the next CHOGM. That will be in the United Kingdom in 2018 after Vanuatu had to pull out of hosting duties because of damage from Cyclone Pam.