Prior to Melbourne, he will play the role in Brisbane from 12 March 2017. In an interview with Limelight, he said that he has had an interest in playing Higgins:
"“From the moment I knew it was Julie directing, I thought this is too good not to do. And I’ve also hankered for a long time to play the role. I like acting in Shaw very much: the intellectual demands and the speed of thought, I find challenging."
My Fair Lady is playing at the Sydney Opera House until 5 November with Alex Jennings as Higgins. Click here for tickets. It's a fun production that is worth seeing (I saw it last Friday).
[slight tangent: Naomi from hellyescharlesedwards has told me that my birthday message to Charles was prescient in a way because I asked him to come to Sydney. My message is the first image in this post. According to the Limelight article he is currently in Sydney meeting the cast and production team.]
Other upcoming roles for Charles are the title role in the sitcom Henry IX (British Comedy Guide), Lucian in the drama series The Halcyon (Sue Terry Voices and ITV) and David Wellsborough in series 4 of Sherlock (@Ruther2 and Spotlight).