Yy to power of attorney - "only" £82 and will save you lots of stress later on.
Hugs. You are at the start of a tough journey but you will get lots of support and help here. And I too have found the Alzheimer's Society helpline great with silly little questions or great big ones.
My mum was diagnosed 9 years ago, so certainly hasn't gone downhill quickly. I spent the first 8 of those trying to get her and dad to move house closer to me. I am so glad that I didn't as now, she is still semi independent in her own home - she can turn the telly on and off, go to the loo on her own, go to bed if she's tired. When she has visited us, or when she had to have a stay in a care home after a fall, she lost all independence, and forgot even the basics. Back home she soon remembered how to do them. If you do want to move your mum, do it sooner rather than later, so that she can build up a familiarity with the layout of her new home.
After diagnosis, mum's council did a carer's assessment for me and offered me practical support which was brilliant in a crisis.
Enjoy the time you have together. Up until last year, we still went on shopping trips together, and giggled a lot. Her sense of humour has remained the same, so as long as I stick to the same jokes we have always shared, she still remembers that they are funny! We have had our dark days, but we are blessed that she is not in pain (she has lived in dread of dying painfully since nursing her own father through a painful and distressing illness, and I am so relieved that her worst fears have not come true.) Dementia does pose lots and lots of challenges, but it can be managed, if you are a close family able to help each other and to access outside support too.
Finally, look after your dad lots. Help him to have a break from her, and try to help him not to feel guilty if he is getting stressed. It is very frustrating at times, so just recognising that for him can help. One feature of dementia can be obsessively remembering certain things, and asking the same question over and over. I used to have a reminder on my phone saying "Get angry with the illness, not the person!" and it would pop up daily, just when I was feeling stressed.
Oh, one other important thing. People with dementia can, with patience, learn new things. I bought Mum a Dementia clock, which is fab - will try to link to it. Best thing I have ever bought. But I had to teach her how to use a digital clock.
And finally, finally be aware that Christmas can be a particularly difficult time for people with dementia. Homes look different with decorations up. Routine can change over the holidays (and routine is very very helpful). People whom you may not remember can send you cards and you feel guilty or confused about how to reply, then suddenly there are presents to think about too. We have coped by putting up fewer decorations and doing so over a long period of time rather than doing it all in one go; asking friends to cut back on card sending (or I hide some of them, so that they just have a manageable few up) and keeping Christmas day very gentle.
HTH. You will get lots of other advice on here. Keep posting