I spent ~10 years moving about annually from apartment to apartment. It wasn't due to lack of resources. I had no sense of permanence, but I would definitely not have said that I was inadequately sheltered.
as long as you had some form of legal tenure over your resident property (this would include rental agreements and long term stays), and the property was deemed suitable by Australian standards for human habitation, you would not have been included in the homeless numbers.
merely being mobile or moving a lot is not likely enough to make you considered homeless by the Australian definition.
however, if you were mobile BECAUSE you were unable to obtain a secure residence and tenureship, or the residences you inhabited were of such a low standard that they didn't meet community standards for acceptable habitation, then you probably would.
I'm struggling to remember, but there would likely be a means/ intention component as well: so FIFO workers, mobile executives are not homeless, but couch surfing students or young people may very well be (even if they spent recent time sleeping under a roof). people camping (or glamping), grey nomads, for example, aren't considered homeless.
that being said, even if these people were counted, it's more of an argument that Australian official numbers should be even lower (though i'd recommend most people to focus of the primary/ first level homeless count for the common "popular" view of homelessness if we're going to reduce a complex phenomenon to a simple digestible stat: but it has the downside that people can then tend to misinterpret low homelessness for other arguments: say, how much poverty there is or how much social housing we need.