In the normal course of events, there is no happier time in a leader’s political life than the months immediately coming to power.

With the strain of the campaign period out of the way, the newly elected leader enjoys opportunities to realise long-frustrated policy ambitions while quietly settling a few old scores with the enemy, and does so in a rare atmosphere of public goodwill.

The latter point is emphasised by the commonly observed phenomenon of the opinion poll honeymoon, reflecting a tendency of respondents to allow that even a government they might harbour doubts about should be given a chance to prove itself as it settles into its new role.

However, quite a few of the ground rules for the experience of a new government seem to have gone out the window since Labor’s wholly unexpected victory in Queensland on January 31.

Reflecting the experience of the former Coalition government in Victoria, Premier Annastacia Palaszczuk has found herself struggling to get her message across amid controversies surrounding a government-turned-independent MP whose vote she still relies on to remain in power.

Together with Algester MP Leeanne Enoch, Billy Gordon became one of Queensland Labor’s first two indigenous MPs at either state or federal level when he rode the Labor tide to victory in the Cape York seat of Cook. However, any self-congratulation within the party at this long-overdue milestone proved to be short-lived.

Gordon soon found himself evicted from the party after it emerged he had been less than candid with it about past criminal convictions, and he has since faced an ongoing barrage of publicity surrounding allegations of domestic violence and failure to pay child support.

Palaszczuk has consistently rejected the notion, but one solution to her dilemma would be the nuclear option of a fresh election, which in Queensland would face no obstacles in the way of fixed terms.

The government has placed itself on an election footing at least to the extent of having moved quickly to repeal its predecessor’s various electoral law innovations, namely voter identification laws and a hike in the threshold for public disclosure of political donations from $1000 to over $12,000.

What’s missing from the government’s perspective is a clear break in public opinion in its favour, with the Billy Gordon imbroglio appearing to cancel out any honeymoon effect for the new government.

Two polls published over the weekend did little to offer further clarity, as their only point of agreement was that the two-party preferred score was 52% to 48%.

But whereas the Galaxy poll for The Courier-Mail gave the advantage to Labor, ReachTEL’s survey for the Seven Network found the Liberal-National Party to be in the box seat just four months after it was dumped from office in perhaps the most spectacular electoral reversal in Australian history.

As well as recording very different primary votes for the LNP — an election-winning 45.6%, according to ReachTEL, compared with just 39% from Galaxy — the two pollsters were sharply at odds with respect to the minor parties.

Whereas Galaxy credited the Palmer United and Katter’s Australian parties with 3% apiece, and still had 6% to spare for other non-Greens minor parties, ReachTEL only found 7.4% support for all of them put together.

A number of distinctions between the pollsters’ methods might be offered to explain the discrepancy — such as Galaxy’s use of live interviewers compared with ReachTEL’s robo-polling method, and the fact that the ReachTEL poll was conducted entirely on Friday night — but perhaps the most telling was a difference in survey design.

Owing to the PUP’s announcement that it will not contest state elections in future, ReachTEL has dropped the party from its questionnaire, and now simply offers respondents a choice between Labor, the LNP, the Greens or “others”.

Galaxy allows responses specifically for the PUP and KAP, notwithstanding the former’s near extinction and the fact that the latter only fielded 11 candidates at the election in January.

Even on the perhaps generous numbers recorded by Galaxy, it is clear there has been no let-up since the election in the long-running decline of the PUP vote, much of which had been concentrated in regional seats where Labor achieved surprise victories, such as Maryborough, Bundaberg, Mirani and Thuringowa.

However, it’s very much an open question as to whether the LNP has been a beneficiary, or if former PUP supporters are simply casting around for a new way to express their hostility to the major parties.

If it’s the latter, the situation becomes even harder to read, given the lesson pollsters learned in January about the fickle behaviour of preferences under the state’s optional-preferential voting system.

On that occasion, the assumption that minor party and independent preferences would behave much as they did at the previous election was defied by an across-the-board improvement for Labor, crowned by a dramatic fall in the number of Greens voters who allowed their preferences to exhaust.

But with the hugely divisive Campbell Newman now out of the picture, pollsters are anticipating a weaker flow of preferences to Labor next time around.

In the Galaxy poll, the improvement in Labor’s position on the primary vote was blunted in the translation to two-party preferred, owing to a model that allocates preferences according to a combined result from recent elections.

Had it been otherwise, the result would have been approaching that of a typical honeymoon poll, with a Labor lead of perhaps as much as 54-46.

ReachTEL went the more obvious route of directly asking respondents how they would allocate their preferences — and while Greens voters were found to be favouring Labor as strongly as ever, the Labor share of other minor parties’ preferences was down by nearly half, with a correspondingly higher rate of exhaustion.

As murky as the picture on voting intention may be, it’s clear enough that Palaszczuk — whose contrite-yet-determined tone in response to the Billy Gordon difficulty suggests she has learned a thing or two from former Labor premier Peter Beattie — is enjoying all the goodwill due to a newly elected premier.

The Galaxy poll credits her with an approval rating of 59%, placing her at around the same level as the famously appealing Mike Baird when he led the Coalition to its emphatic victory in New South Wales on March 28.

However, Beattie was able to translate personal popularity into crushing electoral dominance with considerable help from divided opposition, as One Nation gouged the Coalition vote and sowed discord between the National and Liberal parties while going about it.

Facing a still-united LNP, and with the PUP dying out as a competitor for the right-of-centre vote, Palaszczuk faces the risk that her personal appeal will be trumped by a passive reversion to Queensland’s traditional conservative-voting ways.