I'm no lawyer but when it comes to the law, the burden of proof falls on his shoulders and if it's illegal in your area. If there's no proof, then I think it would be next to impossible for anything to happen. Again, take what I say with a grain of salt. If it came to that point, might be able to turn it around and make it a defamation suit. Consult a lawyer ofc. However, when it comes to social... It all depends on who the people believe. (Anyone, please correct me if I'm wrong.)
Nothing below should be considered legal advice.
The burden of proof isn't his,
it is the state's in the case of criminal prosecution,
assuming sex with an animal is illegal in her state. She should check her local laws. That does not mean he cannot pursue something civil, like suing for ownership/custody of the dog, and in that case, the burden of proof would rest with him, but he also has a lower burden of proof to meet to take the dog away if it
is against the law there, and he doesn't have to wait for a criminal trial to begin or end to make arguments concerning the immediate well-being of the dog or risk of damage to the property, however the law is written there. Even if it is her dog, and even if he can't take ownership, he may succeed in getting it sent to a shelter.
Back to criminal discussion, while she won't ever get convicted on zero evidence and a single witness testimony, this doesn't mean the state can't be pretty humiliating while looking for evidence. And it doesn't mean a DA won't threaten her with as much bullshit as possible to coax a plea deal for lesser charges. Admitting those lesser charges can fuck people up, long term, too.
There's very good odds they won't do anything, because if police followed up every crazy accusation coming out of self-destructing relationships, they wouldn't have time for anything else. There is also the possibility he won't even try to get the police involved.
But the worst case scenario looks like him filing a police report for animal abuse, followed by the police getting a warrant, citing that report for probable cause, and invading her personal space and home in an attempt to collect evidence. That would be a shitty experience.
She should be very careful to not engage him in text arguments or phone calls on this subject. Even saying something like "I don't want to talk about it" in response to an angry text saying "how could you fuck the dog???" could trip her up and bring a lot of fresh hell into her life. "I did not see it" is a better excuse for never replying than whatever she would have to make up to walk back a vague response later.
I am probably being overly severe. But now that she's been caught, she has to be 10 times more careful.