I'm sorry you feel very alone in your current school.
I'm not sure of the Australian school system so I don't know roughly how old you are, when you might be having major exams etc - so my advice is pretty general. However moving mid year is never a good idea unless absolutely necessary, eg parents moving work 100s of miles, bullying. Changing courses & curriculum is always trickier than you think - if nothing else you'll be busy catching up with the school work rather than have time for making new friends.
Breaking into friendships groups will be tricky too mid year - so again I wouldn't recommend it, unless you're being bullied.
You seem to be quite conflicted about a move - understandably so. Is there any one you can talk too - head of year, school counsellor, your parents, a favourite aunt ? You'll need to talk to your parents at some point - so earlier is better than later. It is possible you don't have the freedom to move schools even if you wanted to - just to warn you.
Making friends comes easier to some people and it can be difficult if you're a quiet one. Have you noticed how little kids play together - they will either play alongside and just plain join in or they will say can I play with you ? You say you get along with people which is great so ask one or two girls to join you in going for a coffee (others drinks are acceptable) after school, and take it from there. Approach other quiet people to start with - they may well be feeling just like you and waiting for someone else to move the first move
Not being a sporty one myself, I don't know the dynamics of sports teams. I joined the drama club at school, which is a great way to work on being shy about approaching people, because you're pretending to be someone else. I also sang in the choir. I get these may not be things you're interested in, but to take your acquaintances further you'll need to take a deep breath and step forward and make the contact - just like 3-4 yr old asking to play
By the way - you talk to boys the same way as you talk to girls and if you're feeling uncomfortable talking to the girls at your current school, it could be just the same in a new school, trying to talk to the boys. Basically don't change schools just to get to talk to boys! I know you want to meet boys and that's fine but it's really not worth throwing away your current school work and the loose friendships you actually have for the possibility of chatting to a few boys and then having loads of catch up work to do.
There's lots of research that shows girls do much better in single sex schools - for all sorts of reasons. It sounds from what you've said in your OP that you are having the "normal high school experience" - being a teenager is a time of change and finding your own feet, you own path and it can be really unsettling. You want to meet up with boys, don't want your parents to control you so much and you would like close BFF relationships, but it's difficult to navigate. This is absolutely normal!!!
Don't believe people who says your school days are the best days of your life - load of tosh.
I'm in the UK so I'm off to bed now, but I hope I've reassured you a bit. Please talk with a parent or teacher about how you're feeling