If we're talking geology, then we might as well look at the tectonic plates [0][1].
- 14 or 15 major plates
- 38 small plates
Yet people will talk about 5-7 continents all the time.
Because people will be confused no matter which ill-defined definition is used, I'm switching to the botanical one [2] with 9. It seems to at least have some practical value.
If you leave the underwater parts out, you get a reasonable amount of continents. Sure Arabia and India would confuse people a bit, but besides them it seems to map well to what people expect.
We if are going to get into semantics Australia is actually not mostly covered with sand. A lot of it is dry, but most of the dry parts are covered in dusty scrub and grass lands.
There are actually many more "dwarf" continents (the usual name is microcontinent). The Kerguelen plateau and Madagascar are the two other large ones, as far as I know. Australia and Antarctica are much larger, and in fact microcontinents are defined as being smaller than Australia.
Zealandia is just in the news because it's the latest one to have been formally called that, possibly because it's the largest one (but not enough to be in a different category) and probably also because there's an English-speaking country on it. But it's actually not especially notable.
But I see:
* 1 mega-continent, i.e. Eurasia, which has sub-continents Europe and India tacked on
* 3 normal continents, i.e. Africa, North America, South America
* 3 "dwarf" continents, i.e. Australia, Antarctica, Zealandia
Not only are those 3 dwarf continents far smaller than the others, but one's covered with sand, another with ice, and the other with water.