I think that for every new migrant, we need to really help ourselves. We are the newcomers, so we possibly need to make a lot more effort to try and make friends and fit within our community.
I've been in Perth for 5 months and have not experienced any of the things that you have described. I've made loads of friends and I am always out and about.
Yes, it is hot right now but not so much that you have to stay inside all the time. It does get cooler so choose a time when the temperature has dropped a bit and go out and do things as a family. Knock on your neighbour's door and introduce yourself - that's the only way you'll know them. For all you know, whilst you're sitting there and thinking that they are unfriendly, they're probably thinking the same thing about you and ultimately, someone has to make the first move. Say hello if you see them whilst you're leaving the house and I'm sure that they will respond - Aussies are friendly people, so if you're nice to them, they will reciprocate the gesture.
I find your comment about Perth being sunny really funny cause I always assumed that was one of the deciding factors for moving to Perth - everyone wants a sunny city where you can be out and about as opposed to somewhere rainy and gloomy. What exactly were you looking for in terms of the weather? Maybe you could move to another city where the weather is a bit cooler?
The parks may be empty but that should not stop you from going out (though I always find that there are loads of people in the park close to where I live). What do you like to do? There are so many indoor activities if you don't like the outdoors.
I personally think that you need to make the effort to go out there and mingle - friends will not come to you unfortunately, you will have to go out of the house and find them and if you allow yourself to come up with reasons to stay indoors, you'll just end up lonely and unhappy and it'll become even harder with time to even go out and meet new people.
It's normal to take time to settle in a new city and even to struggle at first to fit in but the key to changing this situation is to put yourself out there and try to integrate into the community as much as you can. If you find a hobby that you like, you will meet like-minded people and start to make friends and once you have an established social circle, you will start to enjoy Perth.
have you considered volunteer work or as shussel suggested, playgroups for your child? That's a really good way to meet new people who have a similar schedule to yourself and shared interest, making it a little bit easier to socialise.
Hang in there - it does get better and good luck. As hard as it seems, make the first step and I'm sure a few months from now, you'll read your post and have a good laugh.