Changes could include locally elected boards in charge of everything from pay and conditions to building maintenance, she told delegates at her UK party's conference in Manchester.
Schools could also be created outside the current system, opening doors to groups of parents, not-for-profit community groups, religious groups and businesses under her new policy plan.
"These are the principles that should underpin education reform in Scotland: a choice in the school your children attend, diversity in the types of school available and a move away from the control of councils in favour of a decentralised system of local school management," she said.
"These reforms we propose will be rooted in our guiding principles of choice, diversity and decentralisation. They will help solve the paradox of hardworking teachers, promising pupils, but often disappointing results. They will break the monopoly of mediocrity that consigns too many disadvantaged children to persistently under-performing schools. They will give an equal chance to every child."
She highlighted a system in New Zealand where schools are self-governing and managed within a national framework. Boards of trustees are elected by parents to give them "a real say" in the way their local school is run, she said.
Miss Davidson also highlighted "charter schools" where licences are issued by the state to a "provider" which operates the school.
She accepted that her proposal will be opposed.
"They'll be opposed by a Scottish Labour party which doesn't share our belief in choice, diversity and empowering teachers and parents. And they'll be ignored by the SNP who will stick their collective fingers in their ears, deaf to anything which distracts from their obsession with separation," she said.
She complained that too many young people leave school without learning the basics.
Her party also wants to create an "opportunity voucher" which could be used by parents to move their child to a better-performing school.
The policy was outlined in a speech to delegates at a Scottish fringe event in the main UK party conference.
A Scottish Government spokeswoman said: "Under Curriculum for Excellence, all children can access an education that gives them the skills and knowledge they need.
"This approach has been praised by international experts including (Boston College) Professor Andy Hargreaves, just last week. This is the right way to improve Scotland's education system and, as a result, there are no current plans to take schools from local authority control."