Bennett asked Hundley what he had said, and he leaned in with his face up next to hers and said it again, prosecutors said in a filing.
Hundley then slapped the child in the face, leaving a scratch below his right eye, the FBI agent's statement says.
Mr Hundley has since moved to North Carolina after being fired amid widespread outrage.
Prosecutors had recommended six months in prison. The judge said he imposed a higher sentence in part because of Hundley's criminal history, which includes a prior assault.
Hundley's lawyer objected to the deviation from the recommendation in the plea agreement and said after the hearing that she believes the sentence is disproportionate.
- with the Daily Mail