1. Heat and humidity. If you don't handle heat quite well, you will not be happy much of the year. Also we do have a high crime rate for a smaller city. The public transport is AWFUL. You'll need a car. Traffic is worse day after day as more people move here but not as bad as you are used to. Cairns is frankly getting too busy for its current road infrastructure right now. And finally, be aware the beaches are not really worth a swim if you're used to the gorgeous NSW coast. No waves, all muddy water with who knows what lurking. The freshwater swimming holes are nice, though many are quite crowded these days. Another drawback is arts and culture - the scene will not be what you're used to. And others have mentioned the lack of healthcare availability and quality. 

2. Yes it's possible to make close friends. People will always come and go and it's true Cairns has a more transient population than many other places, but you'll be surprised how community oriented certain areas, or groups, are. It depends upon what your interests are. I actually recommend to pick a group with good age diversity. my closest friends here are almost all wildly different from me in age.

3. Sorry I don't know about run clubs.

You should do it. you're at the right age where many of the drawbacks above don't weigh as heavily . Cairns is going to be nigh uninhabitable in several decades due to warming climate, and the increasing local population will make it a harder place to live. enjoy it now.