Yes, veterinary surgeons are on the shortage occupations list. In effect, this means that an employer would not have to show that they had tried to recruit locally, and it is much more straightforward for them to obtain a Work Permit for a prospective employee who is not an EEA/Swiss resident.
For your daughter this means that if she qualified as a vet in the UK, she could probably go straight into a Work Permit job as a vet in the UK if she wanted to (and if the rules are still the same, and if vets are still on the list). If she could not arrange that before her student visa ran out, and she still wanted to work in the UK, she could either (1) go home and apply for UK vet jobs from there, or (2) do the International Graduates Scheme for 1 year, and switch to a Work Permit job at the end of it.