Question on legality with Sole Proprietorship and Visa

Hi all,

I am currently working on a WHV that is going to end in a year, and I am planning to work online for my family's online business soon.

I've gathered that it is legal under a WHV, but I plan to switch to a Work Visa with my current employer. I would have to report my online income as business income, and be considered a Sole Proprietor if my understanding is correct.

The work is in a different field than my job here, is it legal to do so under a Work Visa? And what are the limitations? Would it be possible to apply for permission to operate outside of my designated activity?

Thank you so much in advance.