Is income from halal investments taxed differently in Australia?

No. Australian tax follows the legal form of the product and the type of income, not the religious description of it.

• Distributions from a managed fund are taxed on the components in the fund's annual tax statement - income, franked dividends, foreign income and capital gains, each with its own treatment
• Capital gains arise on disposal; the CGT discount may be available to individuals on assets held over 12 months
• Franking credits attach to Australian dividends and are declared and credited in the ordinary way
• Super is taxed inside the fund at concessional rates, with its own rules on contributions and withdrawals
• Sukuk income is generally assessable; the exact characterisation depends on the structure

Purification donations are not automatically deductible - see the purification answer below. For your own position, use a registered tax agent.