In an account of the "horrible accident", the page says Aylee suffered a gunshot wound to the head and was subsequently airlifted to hospital.
According to the Henderson County Sheriff's Office, the shooting occurred in the rural community of Edneyville. An incident was reported at about 2.30pm on Saturday.
NBC News reports Aylee was the daughter of a retired sheriff's officer, Tim Gordon.
According to 911 audio obtained by NBC affiliate WYFF of Greenville, Gordon phoned emergency responders and said his family had a visitor for the holiday who "accidentally left a gun in his car".
"She picked it up and it went off," he said.
Gordon, who retired from the sheriff's office in 2016, reportedly drove his daughter to a fire station because he was having trouble getting mobile phone reception.
She was then taken to Mission Hospital.
According to the sheriff's office, possible criminal charges will be decided by the local district attorney's office or the North Carolina Bureau of Investigation.
Figures from the US Gun Violence Archive show 1046 children under age 11 have been killed or injured by gunfire in 2021, up from 999 in 2020 and between 600 and 700 in each of the six previous years.