That ultimatum is a huge red flag because she's not even contemplating the fact that you might aswell feel homesick once you move to her country. What then?

Emigration is a huge deal, she, of all people, should know it. It's not something that you should do out of fear of losing her but something that you do because you're convinced it's the best possible thing for you and your relationship and she's the one.

Let her dump you, you don't have to leave all of your life behind because she's acting entitled. Also, anecdotal advice, it can take a few years and actual effort to socialise to integrate in your new country. She's a new immigrant, she should give it a little more time before resorting to ultimatums, imho.