Not exactly. The meaning is closer to "live your everyday life". Let's look at it another way. Here's an entry for _go about_ from TFD:
>[go about](    
2. To execute some routine: From my office on the top floor, I could observe all the city's workers going about their business.

_Your day_ just refers to your typical day, your daily activities. So another way to interpret "go about your day" is **execute your *daily* routine**.