American citizen moving to Vienna permanently-HELP

Hello guys, I was really hoping I could get some pointers.

I am a Romanian citizen living in Vienna for 2 years now. I came here because of my job(I have the working permit and all the papers, I am ensured and so forth) and I really like Vienna so farl !

Now the tricky part. My girlfriend is an American citizen and she wants to move here with me permanently in a couple of months(so she is leaving everything and moving to Vienna). I know she can stay up to 3 months without leaving the Shengen area and up to 6 months in a year without having to file for any kind of papers.

Could you help us out, what we have to do once she is here so she can legally move here permanently? She needs a residence permit? I know I can get here health insurance at the Krankenkassa and it costs about 95 Euros/Month - this until she is unemployed and that health insurance is a MUST for permanent residency(don't know if it is called like that, the right to stay here permanently).

We also are hoping she could find a job - how is Vienna on that part of the problem, is it really difficult to get a job/working permit as an american citizen? She finished the university with honours - summa cum laude - Arts and design(don't know if a University degree makes a difference)

Thanks everyone in advance for your help, you guys are awesome!

Thank you

Sebastian