Besides her being on a student visa - if she does not have any
UK ancestry rights whereby she cannot get a British passport or right of abode - then you're probably not going to be able to move to the UK quite that easy
Do either of you have any ancestry rights through a parent or grandparent born in any of the EU countries?
If you do & if either of you qualify through ancestry for any one of the EU country passports - then there is a possibility to get into the UK on either the fiance, marriage or an EEA family visa.
Most of what I just mentioned has been posted & discussed in depth on this forum
Good luck to you
Disclaimer: I am not an immigration expert & anything that I post on visa & immigration is based soley on more than 30 years of personal experience & interaction with the UKBA & Home office.