I have no specific surf camp recommendations, but you can google up some. Most tend to be in N NSW and focus on the backpacker crowd, but may still be suitable for you. The issue you will have is that many camps focus on the beginner, not someone who already can surf a bit. The Surfing Australia centre might be worth looking at, because it has all different levels
https://www.surfingaustraliahpc.com/camps/adults (note they assume this: "To get the most out of our camps, surfers must be able to paddle out the back in 3ft surf and catch waves without any assistance.")
In my view the best time to surf is Feb - May, the water is warm, the air is warm but not hot, the winds are down. North NSW its not shark season...