Moving in together is a big step and your mutual anxiety is normal and not necessarily unfounded. Even if you've been dating a long time, the transition to cohabitating can be a fraught one as you both adjust to sharing space, having less privacy, and figuring out new routines together. Not that the change doesn't bring about lots of positive, fun things, too, but some amount of initial conflict is inevitable.
I would suggest talking together about what your big worries are related to moving in together. This doesn't have to be a long, sit-down, heart-to-heart with the expectation of coming to any "conclusions" about things. You can start by sharing a worry of your own — "I'm worried I'm going to see less of my friends because I will feel badly leaving you at home when I go out." You don't have to talk about whether these worries are founded or unfounded or how you're going to handle them when they come up; the important thing is for you both to put them out there for the other person to hear. Air them out so you have an idea what is concerning each other and feel comforted that you're not alone in your nervousness.
As for your cat situation — there's no way to know how this is going to go. Having a plan in place for the introduction, as you do, is great, but try not to stress until there's a reason to. I've gone through this myself and it did not go so well. It took a few months for the cat spats to end and, honestly, a few years before they were friends. Focus on working through this as a team with your fiancé so neither of you favors your own cat.
p.s. Readers, any advice for dealing with pre-moving in anxiety? Or tips for helping newly co-habitating cats?