My two bob's worth, for what it's worth (huh?).
I don't think we've had a day yet that really defines our nation. I suppose the closest would have to be Anzac Day (to commemorate the terrible loss of young life in World War I, using the Gallipoli Landings as the focus), Rememberance Day (remembering those who died in war and conflict) and Federation Day when we actually became a constitutional nation. The problem with the last one is that it occurs on the New Year (1901).
In all three cases, they already constitute public holidays or at least public significance (Remembrance Day is not a public holiday).
I don't know if the arrival of a bunch of ill treated convicts should constitute our national day, regardless of indigenous thoughts on the matter.
Personally I think we'll have to wait for a severe challenge, which involves conflict on Australian soil, before we can can find a day which claims the national attention.
In the meantime, I think we should just stick with the existing order, until circumstances compel us to fight for our existence as a nation.
Going by the things I see around and about, that may not be too far off (North Korean nuclear ambitions, China's increasing assertiveness, Trump's confusing rhetoric, Russian military growth, India and Pakistan at odds (both nuclear armed), Islamic fundamentalism on the rise (including Indonesia and Malaysia), the pressures of global population growth, super industrialisation, climate change (?), dwindling fossil fuels etc.
And as one British military figure recently put it, Australia would be a glittering prize for some other nations, and he would be very surprised if we are not put to the test some time this century.
From that, we might decide on a day of more fervent significance which will really mean "Australia Day", rather than a bunch of Redcoats on an unwanted overseas posting raising a forlorn Union Jack on the shores of Botany Bay.
But I think it will involve suffering, and a lot of it.