There is no wizarding University(college) because they get jobs based on hwo many NEWTs অথবা OWLs they get. It is explained in the 5th book in the chapter called 'Carears Advice'. So no, they don't need to go to University(college)
The wizarding world doesn't really have colleges. In fifth year, students decide what they want to do and, after they pass their OWLs, they start taking classes based around that. Then they take their NEWTs, and start applying for jobs. Some jobs require extra training (like Aurors), and I'm certain some jobs (like Healers/Mediwitches/wizards) require apprenticeships.
But, over-all, college isn't really necessary in the wizarding world. They get all the preparation they need at Hogwarts.