I don't know design loads in Tasmania and I don't know design values for your timber, but around here (nominal/no snow load) in any wood you would need either tie rods or a serious tension ring design around the eave (like a hoop around a barrel, keeps it from spreading).
Tie rods are pretty straightforward -- they could all go to a decorative/functional hub and radiate out from there.
The tension ring can be done with timber plates at the eave and steel strapping or plating to tie adjacent plates together across the posts. Steel can be expressed or concealed as desired. At 8 in 12, you would have significant loads on those connections at which point strapping won't be enough and you would need a serious weldment.
Or as mo said, you could buttress with another radial colonnade and serious bracing between radial columns. But that's more work and more timber.
Or you could add a column in the center to support the top of the hips, size the rafters to span by themselves and hang whatever hammer beam ornamentation you want to from them.
Short version -- around here, that would be really hard or impossible to do without steel (and meet building regs).
