Hi,
Okay, here's some thoughts. Going to ramble a bit so sorry for the lack of organization.
Sydney vs Austin: Sydney is in another league than Austin (no offense). It's a grown up, world city, a center of commerce for a country and region. It's also very beautiful - not the buildings and such but the harbour, the beaches, the bushland in close proximity, etc. However, that doesn't mean it's "easier" to live in than Austin. That would be the case with any major world city vs Austin: if you went to NYC, it'd be harder to live in, for sure. Same for London, hong Kong, etc. Everything is more expensive. However, as with any big city, it can definitely be worth all the stress and cost! I moved from Houston to NYC two years ago and do not regret it at all. So, as long as you are up for the challenge, the increased difficulty getting around (don't expect to be able to just park anywhere for free like in Austin with huge strip malls and lots), the higher cost (making more money will nullify this logically but it will still annoy you), then it's fine. Sydney is also far more multicultural than Austin.
Australians are friendly but in a very different way than Americans. Really, Americans are different and unique in this way. We have a culture of being very extroverted and outgoing to anyone we meet including strangers. Aussies don't partake in this as much. So, don't expect the smiles and casual smalltalk with strangers you'll find in the US, but don't take it the wrong way either. Once you take the time to develop a friendship with an Aussie it can be very rewarding and I find they take real friendship more seriously than Americans, where it can often be very superficial and sometimes fake. However this quality also leads to a more parochial culture, people live and grew up in Sydney and have a well established group of friends, so they aren't looking to make new friends the same way they would be in a city with a lot of transplants like New York or Austin. A tip - don't try to argue/talk up America to Australians, their culture is all about teasing/joking, but it's a form of affection, so don't take it the wrong way, and don't get obnoxious about America being better or anything because then its just living up to the stereotype overseas of americans. I've seen most expats end up hanging out with other expats (there are plenty in Sydney of all nationalities).I recommend you get work if you can because that will be a good way to meet people. Casual jobs pay well unlike the US so anything will do really.
The hard parts for you - reason I think you may want to reconsider is that you seem very very content and happy with life in Austin. Usually people who have it good aren't going to pick up and leave. You will miss your friends, you will feel isolated being so far away, especially because of the time difference - everyone back home will be asleep after your 5pm or so. You will also have to make new friends from scratch and neither of you knows anyone. So, it just depends whether you are up for this... I don't think you can make the same type of group of friends as back home in the short time you are in Sydney but you have to be okay with sacrificing that to take advantage of the experience.
Minor hard parts - Australia is expensive, but it's not that bad for citizens/permanent residents because they get good support from the govt - free basic healthcare, unemployment and support for hard times, etc etc - you won't get any of these, you have to buy your own insurance, so you're not getting as good of a deal in return for the costs/taxes that locals do. Oh yeah, when you see restaurant prices keep in mind they include tax and tip already, so itll be higher whereas in the US you still add 30% afterwards. No Amazon (try ebay) so there's that too.
Sydney doesn't get that cold but you will feel cold inside your house because homes there aren't built for cold weather (insulation) and they don't generally have heat much. It can be annoying but you'll manage
Your dog - leaving your dog for a year has to be extremely hard. Look into the quarantine laws more closely from what I understand they were modified recently so you only need a 30 day quarantine vs 6 months now. But I'm not sure.
My advice - reason I thought you'd have a hard time is judging by your posts it seemed like you were hoping Sydney would be just like America but with better beaches etc. It's just not going to be the case although there are similarities. You've got to have the right mindset to enjoy this experience: understand what you are giving up and don't dwell on it once you're there, rather, embrace the Aussie lifestyle as much as you can. Get a car, hit up the beaches in town, take ferries, go bushwalking, on weekends take short trips out of town - there is amazing stuff in NSW. Take your holiday leave (4 weeks+) and use it to explore the Reef, Melbourne, Byron Bay, etc.
So I was a bit pessimistic in my original post but I think if you take my advice above combined w/ the fact your partner will be earning double then it should be great. Again it comes down to your mindset.
Note - a lot of this is me giving advice to myself. I'm married to an Aussie and I lived in Melbourne for a few months back in 2012. Back then, I really didn't have the right mindset to enjoy it (and it was winter, so there's that). But, today I just put in my application for permanent residency in australia. I'm drawn to returning and settling there because it's a great unique place and good for raising children. I don't know if itll happen this year but at some point I'll probably live there again. I've also come to appreciate what the place offers as I've gained more experience living outside of my hometown. Really it comes down to mindset and openness to change, just embrace the culture you are going into and try to get out of your comfort zone and you will have a great time!
-I suggest you check out other expat blogs from Americans in Sydney, there's quite a bit. Generally they all seem to love it even if they do go back.
Best of luck and it'd be great if you let me know how it goes once you're there! Let me know if you have any more questions.