The girl's mother, Latasha, told local TV station WATE-TV her daughter had refused the boy's request to play with her puppy before he shot her.
Jefferson County Sheriff Bud McCoig said the boy, whose name is not being released because of his age, used his father's shotgun.
She was pronounced dead at hospital. Ms Dyer described her daughter as 'a precious little girl'.
'No matter how bad of a mood you were in she could always make you smile,' she said.
The boy's family has not commented on the shooting.
Neighbour Chasity Arwood was watching football on TV when she heard a shot ring out and was horrified to see the little girl bleeding to death in the grass.
'That weapon should have been under lock and key, or at least out of hand's reach,' Arwood told WBIR news.
'Trying to comfort her mama and her aunt and her grandma, and her grandpa and her sister and her brother: it's the hardest thing I've ever done.'
Neighbours who were caring for the family's puppies said they seemed to be looking for the girl.
One could be seen laying morosely next to a makeshift memorial of balloons, flowers and stuffed animals on the steps of the family's mobile home.