The overwhelming Irish vote for gay marriage just highlights how far behind the times Australia is.

Britain, New Zealand and many other countries – and now heavily Catholic Ireland. The United States Supreme Court is considered likely soon to support a constitutional right to marriage equality. Yet in Australia the issue remains a struggle.

Ireland was the first country to have a successful referendum but this is not a course for Australia. That’s at least something that Tony Abbott and Bill Shorten agree on. In Ireland marriage is a constitutional matter – here, it is just a question for Parliament. A plebiscite would be expensive as well as unnecessary.

Ireland’s result should inject some momentum into the push for Australia’s law to change.

Greens senator Sarah Hanson-Young said on Sunday she will bring her private member’s bill to a vote in the Senate before the end of the year and she expects it to pass the upper house.

The marriage equality lobby estimates the numbers are close in both houses (assuming a free Liberal vote). But there would be massive lobbying on both sides and so it is hard to estimate the result beforehand.

Besides, important decisions are to be made by both the Liberal and Labor parties before any vote comes up.

The July ALP national conference will consider a proposal that Labor MPs, who at present have a conscience vote, should be bound to support gay marriage.

This question has sharply divided the Labor leadership, with deputy leader Tanya Plibersek supporting MPs being bound and leader Bill Shorten favouring retention of a conscience vote. The conference numbers are unclear, but the result will be bound up in the question of Shorten’s authority.

There are three private members’ bills on the table: besides Hanson-Young’s, the others are sponsored by Plibersek and Liberal Democrat Senator David Leyonhjelm.

Leyonhjelm says the Irish decision has substantially increased the prospect of the Liberals deciding this year to allow a conscience vote and the parliament approving legislation next year.

He pulled the proposed debate on his bill recently when Liberal supporters of a conscience vote failed to raise the issue in the party room. But he plans to talk with them again soon and says he expects “we and they will force the Liberal Party to agree to a conscience vote in the next three to four months”.

Leyonhjelm expects Liberals would prefer his bill to that of Hanson-Young because “they don’t like her”. He is couching his argument not in terms of equality but that marriage is “not the government’s business”.

Abbott’s gay sister Christine Forster says she is “very optimistic” that if and when the conscience issue goes to the Liberal party room the result will be a free vote.

“Then it’s game on,” she says. “My view is, let’s do it sooner rather than later,” before the MPs get caught up in next year’s election cycle.

Abbott on Sunday dismissed the idea of a referendum and reiterated that if the issue came before parliament again, the Liberal party room would adjudicate on the question of a conscience vote.

This indicates that one of the bills will need to be advanced to push the Liberals into a decision – it’s unlikely that those favouring a conscience vote will move without a spur.

Noting that there was a range of views in the parliament, the Liberal Party and his own family, Abbott said that “inside the Abbott family, I’m probably the last hold-out for the traditional position [on marriage]”.

That suggests it is surely beyond time for the nation to move on.