" 'Like a mermaid?' " the girl asks, according to court documents.
" 'Like a mermaid, sweetheart,' " Mahoney replies, according to an FBI agent.
"We cannot forget that for every image or video of what we call child pornography, a child will carry the lifelong scars of rape and abuse recorded for others' gratification," U.S. Attorney Paul Fishman said. "Whether making, distributing or viewing child pornography, the depraved appetites of offenders create a market for the destruction of a child's innocence."
U.S. Assistant Attorney General Lanny Breuer, of the U.S. Department of Justice's criminal division, called the charges against Mahoney "shocking in their depravity."
Mahoney, 32, has been in custody since Dec. 14, the day after the videos were found on the computer of a Texas man to whom she streamed them, prosecutors said.
She is due in federal court Jan. 30, when she plans to plead not guilty, defense attorney Herb Ellis said.
"We are reviewing the evidence, and we are going to do whatever we can to protect her rights," he said.
Mahoney, who's from Manalapan, 35 miles southwest of New York City, pleaded not guilty to similar state charges last week stemming from the same case, her lawyer said.
But court documents indicate that when Mahoney was questioned by the FBI in December, she acknowledged performing a sex act on the child while she was baby-sitting her. She also told investigators that she had streamed live video of one of the sexual assaults to two men using an online chat service and acknowledged filming another assault with her cellphone and sending video of it to two other people, the documents say.
According to an FBI affidavit, authorities found three videos showing her sexually assaulting the girl in October and November. The affidavit describes the sexual assaults in graphic terms. On one, the FBI agent notes, there is no audio. But, the agent notes, "It appears that the adult female is talking and laughing during the video, and it appears that the adult female is talking to another person over the Internet via a webcam."
Two of the videos appeared to have been made in Mahoney's bedroom, the third in the bathtub of her home, the affidavit says.
The court documents make no mention of any possible charges against the recipients of the videos.