I think that taking the dog will be good for you. I know how conflicted you feel about this, and basically everyone who loses a beloved pet goes through this. When I talk to people who decided to adopt another while they were grieving, none of them said they regretted it, although they all said it was hard. They said that while NO ONE can or will ever replace their baby, it filled the silence in the house and gave them a sense of purpose again having another one to love and care for. One friend also said she felt very disconnected from the new dog for the first couple months and still missed her other dog, but over time the bond has grown and she's so glad for her decision to take him. Seeing how much her new dog loves and appreciates her and her husband and their loving home really opened her heart back up from a place of compassion. She says she still misses her first dog though and occasionally cries a year later, which she'd be doing with or without the new dog. So the way I see it is, if not for you, do it for this new dog. It needs a loving home. And in time I'm sure your heart will catch up and it will take the edge off your grieving. Not having another dog for the rest of your life will not bring yours back. I'm so sorry, as I will be going through this right along with you in time. I love cats way too much to not have another one at some point, and I'm being told sooner rather than later is advised. I know I will go through similar guilt, but in my heart I know our passed on babies love us too and do not want to see us suffering, just as we did not want to see them suffering. The love is mutual and eternal. Remember that. Something I have been doing intuitively, without having put rhyme or reason to it until recently, is writing down all my favorite memories of my furbaby in a journal as I remember them, and all the nicknames I had for him, and all the sweet things I remember saying to him over the years. I think I'm doing it not only to honor him, but because I know that with time and other pets, some of those memories may fade a little or get jumbled in new pet memories. Maybe if you do this too it will help you.
Love is eternal & 'death' cannot sever the bond we created. The spirit never dies. The Love, bond, & spirit are ours to cherish always. That is a gift that will never be taken away~