Either can be correct. If you are going right away, you say, "I am going."
I am going to the store
I am going down the street
I am going to my room.
In your example you would say, "I am going to the university" if you were about to go to class.
If you are planning for the future you say, "I am going to go"
What are you doing next year? "I am going to go to college.'
When are you going to the store? "I am going to go tomorrow."
Who are you going to the movie with? "I am going to go with Paul."
In your example if you are leaving and someone says, "where are you going to go?" you answer "I'm going to go to the University."