It's complicated, but the short answer is no. Lying to the Feds is a Federal crime, but in most states - including FL - lying to the police isn't. Of course, obstruction of justice is a crime, and she could theoretically be charged with that, in addition to the DV.
I've said this a lot, but this isn't FHP's finest hour. The fact of the matter is that this is a single car, late night/early morning injury accident and their wasn't a blood-draw done. That's poor police work. Even if they didn't detect the odor of alcohol, drugs or other intoxicants could clearly be in play here.
Also, any rookie cop would have been suspicious of a DV. And, FL law is specific here - if the responding LEO has reason to believe that violence has occurred between two domestic partners, an arrest must be made. The fact that this has gone on now for three days with no statement to the police, reflects very badly on FHP, IMHO.