OP, I am so sorry for your loss. My DH and I lost our dog 3 years ago. He was our first dog, and was like a child to us. The best advice I can share, is what someone told me: Grieve at your own pace, and do what feels comfortable to you.
For instance, our dog passed away 1 week before Christmas, so we already had toys wrapped under the tree. My DH took the wrapped toys, boxed them, and put them in storage. Every time Christmas came, we'd discuss what we should do with his toys: give them to a shelter, keep them for our other dog, or throw them away. Finally, last Christmas we decided to keep them and give them to our current dogs.
For me, it just took a lot of time before things got easier. I couldn't walk into a pet store for the longest time. My DH went by himself to get food for our other dog. I'd say the loss was hardest to deal with the first year. I've come to realize it's not a matter of 'getting over' the death of a pet. Once enough time has passed by, you learn how to cope with it, but it's something that stays with you forever. Just focus on all the happy times you had with your pet. That really helps me.