No, you do not need a full time job.
What lenders care about is your income and your history. They want to see that your income is consistent, reliable, and makes sense over time.
That could be part time work, casual employment, self employed income, or even multiple income streams. The key is showing stability.
If you have a strong track record and your income supports the repayments, you can still be in a solid position.
It is not about your job title. It is about how your income stacks up and how confident a lender can be in it continuing.