VA Girl,
I just went through this! My cat died about a month ago, but the story that really pertains to you would be about my dog.
Last year I got the call during RECRUITMENT (no less) that my dog had to be put to sleep. Molly had been a part of our family for nearly 15 years and we all knew her time was coming, but I thought I'd see her one more time.
My sister was the only one left at home and she'd been the closest to Molly, having only been a toddler when we got the dog.
She was the one who suggested a few days later that we get another dog. Within a month, my parents had a new puppy in the house. While we loved Molly, I think Scout kinda helped my sister heal.
Pets are family and they can never be replaced in your heart... but it doesn't mean your heart doesn't have room to love another animal.
In our case, both our new dogs (yes, my parents got Scout a friend by last Christmas) helped us heal from losing Molly and we saved them from two local shelters.
I guess I understand that it is important to have time to grieve, but new animals have lots of love to share to help 'fill the void'. For me, I was pretty upset about Molly and getting a new dog was a bit painful until I got to meet Scout. I still love and miss Molly, but having two(!) dogs has helped my family through the pain.
You and your family are in my prayers as you grieve for your dog. Good luck!