Yes, it’s legal. He became King the instant his mother died with all the rights and duties that come with it.
The Coronation is an important ceremony where he takes certain oaths (although he also took his first oaths as King the day after the Queen died at his Accession Council) but it is basically ceremonial in terms of his legal powers.
There’s also no requirement to be King to knight somebody - he knighted people as Prince of Wales, and other members of the Royal family also carry out these investitures from time to time.
Is ir true Australia is going to remove him as monarch?