Hi Cheryl,
First, a disclosure - I work at the University of Melbourne. I was previously an admissions tutor and academic in other universities (mostly in the UK), so I know this sort of enquiry well.
The UoP is relatively lowly ranked as you noted. It is an established private university, but it isn't anywhere near the Ivy League level - that's the elite private universities in the USA - and it isn't as strong as the main University of California state universities either. In terms of research, it is not a big hitter.
Melbourne has a strong Engineering school, bioengineering included. We're top thirty in the world, whereas UoP is not usually ranked in the top 100 in the USA. Our engineering courses are increasingly well regarded for the quality of their teaching. Melbourne is also, as a city, very active in the bioengineering industry. I'm not sure that that's true of any of the UoP's campuses.
I'm happy to put you in contact with some of my colleagues in Bioengineering - I'm a computer scientist myself.
I hope this helps,
George