Tory leadership hopeful Ruth Davidson has said she would support moves to allow gay marriage in Scotland, and said she “would love to see” free schools opened in Scotland along the same lines as has been introduced by the UK coalition government.

Taking questions at the launch of her campaign, Davidson said that she would welcome equal marriage legislation provided it allowed those conducting ceremonies to opt out on grounds of personal belief.

Davidson also suggested that rival candidate Murdo Fraser’s plans to reform the Scottish Conservative and Unionist Party had “drifted” and become less radical since they were announced.

“I have no interest in change for its own sake,” Davidson told assembled media and supporters.

“Under my leadership, there will be no existential crisis, no wringing of hands. Instead, I want people proud to call themselves Scottish, Conservative and Unionist – as I am proud – to join me in explaining how our ideas for Scotland can make a difference.”

In his introduction, fellow MSP John Lamont said that the Tories under Davidson would reach out to “young, professional, patriotic and aspirational” Scots, who had never voted Conservative and who sought a “different kind of politician”.

Davidson – who became an MSP at this year’s election – referenced her previous work as a journalist several times, first claiming that it had involved “asking [Alex Salmond] the tough questions, pressing him for answers”, then using an anecdote from a foreign assignment to describe her pride at being British.

“I was in Kosovo to spend a short time with the Black Watch who were serving out there. I saw young men – men I’d gone to school with in Buckhaven – or who’d gone to schools nearby. And I saw them protecting innocent civilians, defending people’s freedoms, rebuilding a shattered country. I have never been so proud as watching a patrol come in, put down their weapons, have a brew, pick up picks and shovels and sledghammers, get back on a truck and head off to spend their down time, when they could be resting or emailing home, volunteering to rebuild an orphanage.”