Paul Demetro, 30, was driving a 2010 Audi through an intersection at 4:40 a.m. when he fishtailed the car, sheriffs said in a news release.
Deputy Sheriff Greg Turzer pulled the car and after an interview with Demetro, the driver, determined he was "under the influence of alcohol," the release said.
Also in the car was Demetro's daughter, the child's mother, and a passenger, a 29-year-old man, sheriffs said.
Demetro was arrested on charges of aggravated driving while intoxicated, a felony, endangering the welfare of a child, unlicensed operation of a motor vehicle and a seat belt-violation, sheriffs said, because the daughter was not restrained properly in her car seat.
The girl was released to her mother, who was driven to their destination in Selden by the passenger, who was sober and licensed, sheriffs said.
Demetro is scheduled to be arraigned Tuesday at First District Court in Central Islip.
Leandra's Law was passed in 2009 after the death of Leandra Rosado, 11, who was killed in an DWI accident after the minivan in which she was a passenger crashed on the West Side Highway in Manhattan.