Certificate 3 or 4 in Fitness does not include Pilates, therefore the scope of practice will not cover you to teach Pilates without additional Pilates-specific training.
As well as a comprehensive first aid certificate (e.g. HTLAID011) ​​you will need Professional Indemnity and Public Liability insurance. Your insurer will also require evidence of your Pilates training before insuring you to teach.
The PAA have minimum standards for Pilates instructors and members, with a Pilates-specific qualification of either Certificate IV for teaching mat/reformer group classes, or a Diploma in Pilates instruction for teaching studio.
Our recommended Professional Pilates training providers and courses can be found here: https://www.pilates.org.au/education/