It is a little subjective because different employers have different views. But of course having a degree from a well known university helps in the long run if you don't mind the fees. It helps more when you are a fresh graduate to get into big firms (and more demanding roles which helps to kick start your career). But once you have years of experience, people focus on your experience instead of your degree.

If you intend to study in Australia, do look up on G8 because they are the best universities in Australia. You could study in Monash or Swinburne and then transfer to their Australian campus later on to save cost (e.g. 2+1 twinning program). Or you could study in any local private universities (INTI/APU/etc) and then transfer to their oversea partners. You have to check which oversea university have partnerships with them and whether you are okay with those partners.

Also, I see that you have interest in going overseas in the future. If that is the case, studying in an oversea university will help as well (especially when you want to apply for PR and etc). Because when you apply through immigration, there are background checks which will evaluate where do you graduate from (you may get bonus points).

IMO, APU's quality has degraded over the years. Back then they were known as APIIT and is famous for IT degree courses. I would go for Monash if money is not an issue as that they will have better quality lecturers. But you will have to research on this as I don't know if they are still maintaining the quality now.