She will be treading a tightrope or two, and will be under very close scrutiny from all of Australia.
The first tightrope she will be walking is that of the Labor Party, which has a history of setting women up for a fall. I have wondered why a Leftie would be pushed into the job by the Right, and also predicted on Yahoo 7 that she would be installed before the next election for one of several reasons:
firstly, as a 'lame duck' with the very real chance that Labor would lose; in which case she and women would take the flak from the Party;
secondly, for Labor to demonstrate to the female vote that they 'really are doing things for women', unlike the Opposition;
thirdly, simply to give a woman a shot at the title.
The second tightrope is that the Australian public will be watching her like a hawk, and if she shows any signs of radicalism from her Student Union days, cited many times as Communist, they could just very well rise in anger. She will also, as a woman, again with that Student Union background with its strong focus on feminism, be under extreme pressure from her feminist allies and friends to push through some more (and I use that word deliberately) nasty legislation to 'equalise' women by 'unequalising' men. I would very strongly advise against anything remotely like this.
On the other hand, however, if Labor win the next election - she will have several years to push any agenda she wants - under that ongoing delusion of 'The Divine Right Of Politicians' that they somehow have a 'mandate' to do whatever they want, regardless of the electorate. The biggest problem with that is that, under our essentially bi-partisan government of two Parties, any unwanted and even wrongful or illegal things pushed through (such as more violent laws against men, such as DV laws, EEO, and so on) is never set to rights, but allowed to continue.
So - I figure La Gillard will have to suddenly find a great deal of conservatism to please the Australian people, and will have to rein in the natural impulse to trumpet a 'victory' and 'take a victory lap' etc, as has been so honoured by recent incumbents in her seat. Oz is also sick and tired of PMs and PMs who constantly wander the world at public expense, and leave their deputy to fill the vacancy at full pay.
I believe the Australian people have had it up to their back teeth with selfish and irresponsible government, and are seriously seeking a different approach for the future - any failures in providing good government, through misguided moves in favour of specific groups etc, will see La Gillard go down in history as the women who broke Labor and possibly even the current Australian way of democracy.
I would also suggest that since Kevin Rudd was 'elected to the job', and La Gillard was not - many will hold that against her, and it could well open the way for a Republican movement, since the people want to see their head of government remaining the one they 'voted into the job', and not be controlled de facto by party politics and party power brokers.