Fundamental principle of democracy is equality of all people in society.
Fundamental principle of monarchy is superiority of monarch and his/her family over all other people in society.
Are democracy and monarchy compatible in principle?
Can Australia claim to be a democratic society while having a monarch as a head of state?

yeah its too insane for words aint it
were a colony founded by royal charter
via an axct of and approved of by the brit parlement
[ie shouldnt be allowed into the un cause we arnt a 'n']
yet we were heavilly involved in founding it

we got a so called queen
but the queen isnt 'the crown'
we got crown lands./..but they dont belong to the people

we got one lot that claims to rule by right
[or by god given deed of grant]
telling the peons when to go and die.
when to pay taxes

running arnmed forces
for when the peons rebell
and thinking of ever more taxes
to invade other counties[nations]..other kingdumbs

then we got the ones we voted for
that come from a selected elect pool..via a two partyy system..that lords it over the peons..taxinf us to death with ever more levies taxes and compulsory uni-lateral contracted terms and ever more obligations in lue of rights or dividend]..or fair share

no 9 cant se the difference cause there isnt
heck im not hurting you...they are
no its not me its them

plausable deneyability
its the ctown..no its the queen..no its the un
no its the world bank..its \federal govt..no its state..no its local councxils//no its ngo's..no its you..heck its me

now bow down
bend arround
i got something big
just for you

yes we do aqway with big kings
and elect little kings
per suburb..or even per street
they are there to replace ALL other kings/govts/councils

HE/she..is the only one who cant collect our tax

how about it your majesty
sign the sun treaty
adopt the wikseed

bah why bother

when we vote
we stand under[claim lower standing]
put in place a trustee to manage our affairs and estates
we are legally imbisiles..[wards of the court's..in compitant to manage our own affairs]..but im sick of explaining to slaves why they are slave..enslaved]

Would any one care to tell me I am wrong.
Royal family's began first as tribal Chieftains.
The strongest boldest even brightest at first ruled.
Then passed that rule on down the family.
At times inter wed others imported with some relation ship to past rulers after part of that family tree fell over.
Why then do we bother electing our politicians?
In some well told story some country's leaders end up back at the foot of the English Royal Family Tree.
So no, elect our leaders, no excepting a family that has no reason and seems in all of history to have inbreed to keep a power that is not theirs.
A any dinner ,this tour or any day, our Queen? not mine actually! only has to put her purse on the floor and people will whisk the person next to her away as unsuitable to sit near her!
I am not amused.

Can Australia claim to be a democracy while having
a monarch as Head of State?

Yes of course.

Australia is a federal nation. It is also a
parliamentary democracy.

Dennis Pryor in his satirical dictionary,
"Political Pryorities: How to get on top of
Australian Politics," summed it up beautifully,
with his tongue firmly in his cheek:

"The illusion that the Australian government works,
or should work, on the same principles as the
British government. The similarities between the two
systems are largely those of decor, like the use of
the mace. The major difference between the two systems
is that Australia is a federation, a concept totally
incomprehensible to the British.An appeal to the
'Westminister system' is a slogan used by
Opposition parties in an attempt to trick their
opponents into foolish resignations."

By strictest definition, the concepts are not compatible, as democracy means 'public rule' and monarchy means 'monarch rules';
In the case of constitutional monarchies (eg us), the monarch simply does not actually rule anything and serves as a figurehead, while the people in practice actually rule- so it is possible in the way we do it.

Though personally I'd rather not have a ceremonial head of state that requires our own upkeep. Having said that, as we do not actually pay the British Royal Family a cent ourselves, I would be quite happy ditching the Governor-General alone;

When we can have dreadful, badly designed & built buildings listed by the national trust, [what or who ever the hell that is], as important heritage, surely the heritage of us as a people is worth preserving.

The main argument against a monarch is that one day, one of them might turn out to be like Julia.