Hiya Rhosalie and welcome to the UK...
If you have the vignette visa ie the paper sticker in your passport then that is fine until your next FLR (M) in 30 months time, just check expiry date on visa the new type only have 30 days for you to get a brp card the older ones which I believe in your case should have an expiry around 30 months from now and if that's the case no worries.
Definitely register with dentist, doctor and also get yourself a national insurance number from the local jobcentre and also get your name on documents like council tax, utility bills, rent agreements etc, for future use for next visa in 30 months as evidence of cohabitation.
Sure others will be around with more info on this long and tedious journey but everything will be fine and I wish you both all the luck in the world, God bless. ..![]()