Thanks for all your responses. Your views have given me a lot to think about.
I'm still in two minds about it but I think most likely we will be going down the public primary then private high school route.
Benefits
Cost saving. We will struggle to keep paying the fees for the next 15 years unless our income increases significantly.
Opportunity to start again socially/avoid getting pigeon-holed
Location is far more convenient
Negatives
Potentially good friends being lost
Depending on the number of new students, difficulty fitting into established social groups (question to ask when we see them!)
Better academic result for private school compared to public. I do think this depends a lot on the student though so I don't place a high importance on NAPLAN results.

I believe that kids will achieve their best if they are happy. If they are being bullied and hate going to school their results will suffer regardless of where they go. I can see the benefit of changing schools to remove the influence of bullies. I have my own experience to back it up. Years 5-7 for me were the worst of my life - a group of 4 girls who were consistent serial emotional bullies. The worst type IMO. At least 2 girls changed schools because of them. Going to high school was great for me because I got away from them - I went from public primary to private secondary and they went to public high schools. But everyone was in the same boat. That particular school started at year 8 so everyone there was new and came from a large variety of schools and even out of town as it was a boarding school. I wouldn't hesitate to change schools in this situation.

I spoke to DH and he has agreed to look at the private school that I'm favouring. I will ask about how many new students start in year 7/8 and reconsider then. I will also visit the public primary school so I can get a good feel of the culture of both schools so I can compare.

It is such a hard decision. I wish I had a crystal ball so I could see the future lol!