As winnie says, the blue badge is for the person who is "disabled" and they must be in the car whenever it is used.
As I understand it, AD alone does not qualify you for a blue badge, only if there is a mobility restriction involved.
For example we now have one for my mum as although she can shuffle along unaided, after a couple of hundred yards she is so off balance (because of the effects of AD) that she either falls or it can lead to an epileptic fit. However that has only been in the last year and she would not have been entitled to it for the previous 5 years when her AD was first diagnosed.
If you do apply (and although it is a national badge it is down to individual councils how/if they issue them), make sure your GP makes it very clear why she needs one. Always fill the form in as though it is a worst day scenario.
Good luck.