If I said "I brush and it's off to the shower"
Firstly,
"I brush" refers to his teeth. I can tell that person means they brush their teeth before they go take a shower.
"off too" - to be off to - Fantastic Question! - I love this because this is not something you learn in school
This means simply, to go.
Examples
I am off to the kitchen for a snack! - I am going to the kitchen for a snack
Off to school you go , child! - You are going to school
And they are off! - (if this is a competitive race setting)
"I brush my teeth and then it's off to the shower" - I go to the shower or Better -> I go take a shower
excellent question and good for you for hearing this one!
Hope this helped