Julie Maynard and Frances Bodel kissed in the public gallery of the ACT Legislative Assembly just after the bill was passed in October 2013.

The Canberra Times described the image as one "every Canberran deserves to see" when it published the photo, breaking the assembly's rules which ban cameras from focusing on people in the gallery or recording any "protests, demonstrations or disturbances".

Now the Belconnen couple have finally tied the knot, taking advantage of Vietnam's marriage law passed in January, abolishing a ban on same-sex marriage.

Ms Maynard said the couple had an "absolutely amazing" day, marrying on a traditional fishing boat in Hoi An on Monday, but were sad their family couldn't be there.

"We will get married in Australia when it's legalised because we want our family there, but they completely understand why we wanted to do it," Ms Maynard said.

"We decided to have a combined holiday/wedding/honeymoon."

Ms Maynard said it was sad to see conservative countries like Ireland pass same-sex marriage legislation while Australia languished behind.

"We've known each other for three-and-a-half years and we can't get married," she said.

"We love each other just like everyone else, we've got a house, careers and we don't feel like we're treated as equal."

Social Services Minister Scott Morrison defended opponents of same-sex marriage such as himself on Tuesday, saying they were not "homophobes" and called for Australia to take a "breather" on the debate.

Mr Morrison told 2GB people should not presume a change to the Marriage Act was the "only answer" to same-sex marriage.

He said there was a "a range of options which haven't been ventilated" including Liberal MP Philip Ruddock's suggestion for a French-style approach where civil unions are registered at the federal level, and marriages remain the domain of religious institutions.

Former Howard government minister Peter Reith backed a plebiscite on same-sex marriage to take the issue out of politicians' hands as Coalition MPs continued to bicker over calls for a free vote.

Although Vietnam's January laws abolished fines imposed since 2013, the government does not recognise same-sex marriages.

But the move is still paying financial dividends for the nation with wedding planner businesses springing up to accommodate foreign couples' marriages.

"The amount of couples going overseas and taking their pink-dollar with them is crazy," Ms Maynard said.

Ms Bodel's mother, Elizabeth Bodel of Weston, said she was thrilled for the couple, but it was shame they could not get married at home in Australia.

"It's what they have wanted for a long time, so we are all really happy for them," she said.

She said politicians needed to "hurry up" and introduce marriage equality.