Scuba Diving the GBR in November

[thenotebook]

Hello! I'm traveling to Cairns and arriving Sunday afternoon Nov. 22nd and staying through the end of Tuesday Nov. 24th. I'm traveling with a group of people some who scuba and some who would like to snorkel.

I'm a scuba diver. I'm wondering if you have any recommendations on finding a scuba dive shop that goes out to the GBR for a day trip or overnight that doesn't take too many people (preferably <10 people). The only one I can find online have to be under some approval of Australia Scuba Something or other. I would like to find a small local shop with low overhead costs that would be what the locals know / hidden gem. We don't have a place we're staying at yet we're thinking Cairns or Northern Beaches Area. Also, how's the weather at this time?

Thanks for your recommendations!!