Meh, I think she'll loos much of her unpopularity once the carbon tax debate is over, but I think that the Coalition will still be the natural favorites in the 2013 election, although a lot can change in two years!
She's doomed. I'd be surprised if the current parliament even lasts its full term.
Why would that be exactly?
Because the carbon tax debate isn't likely to go away anytime soon, and even if it does, the Coalition could run a campaign pointing out how Gillard was dishonest in her past statements about implementing a carbon tax in the first place.