I would not.
The Australian government seems entirely incapable of creating any technical project of a decent size correctly. The list of disasters is quite long, but a few from recent memory are ones such as the census website which collapsed when people tried to use it [0] and the myGov project which has had so many data breaches [1].
Atop of which, the government's usual response to someone exposing flaws, is to attack them.
Whilst I don't want Google or Facebook to have my data, because they will use it in ways I don't appreciate, my government will leak it. And then claim it wasn't serious and excuse themselves from any repercussions.
[0] https://www.abc.net.au/news/2016-08-12/census-2016-site-up-a...
[1] https://www.smh.com.au/technology/revealed-serious-flaws-in-...
[2]
[1] https://www.theguardian.com/technology/2020/may/03/home-affa...
1. https://www.wired.com/story/australia-encryption-law-global-...
[1]: https://www.eff.org/deeplinks/2020/06/senates-new-anti-encry...
I didn't say the US Senate is a lot better, but to be completely fair there isn't a backdoor law in the US yet. It's possible Australia was the testing ground for that type of legislation though.
Heck, that's exactly what the ASD did when the vast majority of people were screaming about employees being individually targeted by the legislation (which wasn't accurate). Now, the ASD also did misrepresent the legislation too -- but now it's less obvious to the general public who is actually being sincere.
However, it would require your health professional to upload data to the service - and most have simply refused.
But to actually check if one's MyHealth record exists and has data, one must first opt-in to MyHealth, which is a bit chicken/egg.
https://www.accc.gov.au/focus-areas/digital-platforms/draft-...
[1]https://en.wikipedia.org/wiki/PRISM_(surveillance_program)#M...
Being legally compelled to provide data isn't the same as being 'willing'.