Our last cat died almost seven years ago, at the age of almost 21, and that was the first time in my life that I'd lived in a 'petless' home!
I've lived with dogs, cats, guinea pigs, hamsters, gerbils, rabbits, goldfish, tropical fish, both fresh and salt water, and at one point, we even had two geese, named Daphne and Diane!
The thought of living without a pet was unbearable, but DH made me promise to do twelve months before getting another animal, just to give me time to see what life was like without the ties and responsibility.
We're still a 'petless' household, but I'm never going to say 'never'! At the moment it's easier for us to not have a pet, but in the future.....maybe!
So, MawBroon, my advice is to wait a while, Grace was such a big part of your life that you need time to grieve for her. Then give yourself a few months to see how you feel, it's far too soon to be considering another dog yet. 