It accused the Scottish Government of "obsessing about breaking up Britain" rather than focusing on practical issues.
But the government claimed it was "very encouraging" Stirling was enthusiastic about the policy.
The move will begin in January and comes months before it becomes a national policy to increase the amount and flexibility of free early learning and child care from 475 hours-a-year to a minimum of 600 hours for three and four-year-olds.
The Government estimates families will save costs equivalent to around £700 per child in funded early learning and child care under the national proposals, with around 121,000 children benefiting.
Stirling's pre-emptive move comes amid an ongoing dispute, including strike action, between the council and unions over claims staff have been offered a 0.5% pay cut and been asked to work an extra hour a week.