OK, NOC only applies to Work Visa, so family visa is OK.

Changing passport won't work if she wants to work though I think as this would likely be flagged up by the fingerprints which won't change with the passport.

Also if you are having to change the Citizenship, i.e. she does not have a British Passport, and it is your intent to get her one, I think she needs to be in the UK pretty much permanently for 2 years, after marriage, before taking the citizenship exams partly to prove I think that it is a commitment to become a Brit rather than just a marriage of convenience. Could be wrong, but I know the 2 years in UK was easier than the alternative for a friend who did similar, though he met her in China and took her to the UK before coming to Qatar, she stayed there to complete the 2 years, with occasional visits.