The council was asked to consider cutting the length of summer holidays from six weeks to five.
The other week would then be moved to another time in the school year.
The authority's children and young people scrutiny committee will now look into possible dates and consider the wider implications of the move.
The proposal - put forward by Gabalfa Liberal Democrat councillor Ed Bridges - highlighted what he called the "disproportionately expensive cost of holidays" during the traditional holiday break.
"Currently families taking holidays during school term time can do so more cheaply than during allocated school holiday times," said Mr Bridges.
"From my own experience the cost of going away for a week during October half term is basically double what you would spend on the same holiday in May during the school term time.
"Families are often having to make a very difficult decision of whether they go on holiday during school term time and pull their children out of school, or in some cases not go on holiday at all if finances don't allow it."
It was suggested extending the October half term to two weeks could help families save money by booking travel outside peak periods.
A Welsh Government spokesman said the education secretary Kirsty Williams would not be using ministerial powers to direct local authorities and governing bodies what their term dates must be.
He said the government was "pleased to see that they have successfully worked together to ensure harmonisation of term dates across geographical areas for 2017-18".
"Schools have a discretionary power to authorise up to 10 days' absence during a school year for family holidays during term time," he added.
Cardiff councillors have voted to carry out a "detailed" study on changing school summer holidays.