The first thing to do when changing your business structure is to apply for a new TFN and ABN under the partnership business entity. It's not too much of a big deal if you don't cancel your current sole trader ABN, but it just means there'll be more paperwork involved for you as you might still need to complete your BAS statements and other tax/financial reporting. 

In terms of tax, it's similar to paying tax as a sole trader. Each partner reports their share of income earned from the partnership in their individual tax return. You will pay tax on your share of the partnership's profit (along with any other personal sources of taxable income) based on your marginal tax rate. You may also be eligible for the small business tax offset. Visit the ATO’s website for more information on partnership tax: https://www.ato.gov.au/Business/Starting-your-own-business/Before-you-get-started/Choosing-your-business-structure/Partnership/

It's always best to get expert advice from a registered accountant or tax accountant when it comes to things like business restructuring if you have any doubts or concerns.