My elderly Mom with slight dementia lives with me. She has had 2 dogs in that time and both got very ill and had to be put down. The last one had accidents in the house and Mom fed her several times a day because unless I was home she would forget if she had fed her and forget to let her out. I have explained that we are not getting another dog because her memory is slipping and I don't want "accidents" all over my home, and I get my heart broken when we have to put them down. Her last dog just got put down a week ago and all she does is cry and whine because I won't let her have another dog. It is seriously like having a small child. I need suggestions.
If her memory will allow it, I might have to fib about it. Have you considered that the reason she keeps repeatedly asking about the dog is that she forgets the answer. She may continue to ask, since she has forgotten what you said. So, I might give her some reason the dog hasn't arrived. I know some people might disagree, but, there is never going to be a reason that she will understand and accept, so why not just keep her happy, believing that one day she will get one. Eventually, she will not remember about it. I know that's sad, but, I"m not sure of any other option. Maybe, you'll get others.
You can always get her one of those lifelike dogs that actually moves like it's breathing. It comes with its own little bed and looks very lifelike. They are called Perfect Petzz. You can find them online. They are very cute and worth a try if you think she would accept it. They come in cats and dogs.