Dawson and Liddelow's marriage, conducted by a celebrant before a small group of friends and family, became official at 12:04 a.m.
Three security guards were on hand to ensure that the wedding party maintained an appropriate distance from Parliament's front entrance.
"I'm just very, very happy," a tearful Dawson said after the ceremony.
"I hope that the High Court sees fit to allow these laws to stay," he added.
Earlier, Dawson said he and his partner decided that they didn't have a moment to lose before marrying.
"We don't know how long we've got in the sense that the High Court might overrule the laws next week, so we thought: 'let's do it straight away and let's have the maximum amount of time being married,"' he said.
Canberra's iconic Telstra Tower was illuminated with sequential rainbow colors from midnight to mark the first same-sex weddings.
The tower provided a colorful backdrop for Alan Wright's ceremony when he wed his 30-year-old partner Joel Player on an island in Canberra's central Lake Burley Griffin after midnight.
He wasn't sure whether his marriage was before or after the 12:04 a.m. mark, and he didn't care.
"I'm proud to be part of the first couples married in Canberra," said Wright, a 34-year-old civil servant.
Wright hopes that even if the High Court rules against gay marriage, the judges will allow all marriages conducted before their decision to stand.
But Sydney University constitutional lawyer Anne Twomey said that wasn't a possibility.
She said there was a range of potential outcomes for the court challenge. It could rule that no state or territory could legislate for gay marriage, or that the ACT alone could do so.
If the court ruled that the law can survive with amendments, Twomey could not say whether the marriages this weekend would be legal, or if the couples would have to marry again after the legislation was amended.
Sharyn Gunn, the celebrant who married Wright and Player, said same-sex couples she had spoken to were evenly divided between those who wanted to get married as soon as possible and those who wanted to wait until after the court decision.
Under the ACT legislation, couples have to give 30 days' notice of their intention to marry.
The advocacy group Australian Marriage Equality said at least 20 same-sex couples are marrying in Canberra this weekend, including its deputy director, Ivan Hinton.
Hinton, 38, is marrying his Malaysian-born Australian partner Chris Teoh, 35, on Saturday afternoon. The couple wed in Montreal, Canada, five years ago, but the marriage is not recognized under Australian law.
Hinton said he never considered waiting for the certainty of the High Court decision before tying the knot again.
"It would only be worse for us to realize that we'd had an opportunity and we'd missed it," Hinton said.
Gay marriage has legal recognition in 18 countries as well as 16 US states plus the District of Columbia.
-AP
