In her role as Head of the Armed Forces, the monarch, 94, spoke to General Sir Mark Carleton-Smith on Tuesday morning.
The pair discussed how the Army has continued to support communities throughout the UK amid the coronavirus pandemic, as well as carrying out operational duties overseas.
Speaking to Australia from Windsor Castle, the monarch held a video call with the Governor of South Australia Hieu Van Le, and Steven Marshall, Premier of South Australia.
The sculpture, which depicts the Queen in a coat and hat carrying her trademark Launer handbag, has been installed in the grounds of Government House in Adelaide.
Prince Philip was transferred from King Edward VII Hospital to St Bartholomew’s on Monday morning.
The duke, who turns 100 in June, was transferred for treatment of an infection and observation for a pre-existing heart condition, Buckingham Palace said.
In a statement issued on Monday, the Palace said Philip was “comfortable” and “responding to treatment”, but was expected to remain in hospital until at least the end of the week.
Phillip was admitted to the hospital on February 16 after feeling unwell at Windsor Castle, making this his longest ever stay in hospital.
In June 2013, he spent 11 days in hospital after surgery on his abdomen.
Since his admission to hospital, the duke has received a visit from his eldest son, the Prince of Wales, who was seen arriving on February 21.
Last week, the Earl of Wessex said Philip was "a lot better" when it was announced the duke would spend several more days in hospital being treated for the infection.
Prince Edward said his father was "looking forward to getting out" and the family were keeping their "fingers crossed".