I currently live in Australia and trade stocks/futures independently, which makes me self-employed. Is there a business visa I can get to come to Singapore and then apply for PR later?

To become eligible for PR status under the PTS scheme, you must be an S Pass or E Pass holder and work in a Singapore company. You can try the investor route under the GIP scheme, but that requires you to make significant investments in the Singapore business landscape, and you must also have a proven track record (Normally not easy to meet requirements).

You can think of registering a company in Singapore and apply your Employment Pass under it. Once approved you can relocate and after 2-3 years apply for your PR.