The problem was not whether Gillard should but what was announced

Comments on Christopher Pearson “Cabinet leaks show depth of Gillard's problems”, 31/.07/2010, http://www.theaustralian.com.au/national-affairs/polling-centre/cabinet-leaks-show-depth-of-gillards-problems/story-fn5asavh-1225899248390
It is not wrong or problematic to announce a new climate change policy by a new prime minister, given that Rudd and his government had been in serious trouble by his ETS retreat.

However, what has been announced is a problem. Instead a convincingly effective and practical policy, she announced almost no change to her predecessor’s policy. Worse still, adding a talkfest - a citizens' assembly.

Given that they were prepared to go with the/a mining tax, what she could have done is a modest carbon levy/tax with redistribution to consumers, i.e. all residents to offset the effects of the levy/tax.

That could have distinguished her from Rudd's policy and recapture the support of the majority of the public.

So two of the 3 issues she identified at the time of her prime ministerial address have not been satisfactorily dealt with by her even though the handling of the mining tax wasn't too bad.

Of course, if those leaks are true her political judgement may be an issue for her leadership as prime minister in the longer term.