historically, the phrasal verb in the UK was to "go off". And over time it got reduced to the use with the verb "to be" such as "im off" "im going off to university" and "Im off to University" are both correct. I dont think these are used in American English. Perhaps someone else can clarify.

Off to ... means to leave for somewhere I am off to the shops.

It means "Okay. I am leaving for the university now." / "Okay. I am heading to the university now."

Hi. "Off to" most of the time means "going to" and that fits in so well with your sentence.