I'm interested in becoming a veterinarian for the army and was wondering how the process goes from Uni to army vet?

The process for applying as a veterinarian would depend on the pathway you wish to take. If you are already qualified you would enter as the professionally qualified route (PQO), if you are still at university you may be able to get on to one of the other programmes available. If you Google Army fund university you would find more information there. The process is all done online and everyone needs to pass the same steps of the application to progress as this would be an officer role you would need to look at the officer entry route or the PQO route as it is slightly different to the soldier route.