First, I'm sorry you lost a good friend; a lot of people think it's silly to grieve over the loss of a pet, but if he was an important part of your life, then of course you need to grieve. Second, even if you wanted to replace him, you couldn't; there's no other dog anywhere who would be exactly the same. Third, allow yourself some time. When I lost my German Shepherd to cancer after having him as a great dog for 11 years, I wasn't ready for another dog until about a year later. Now, I have two. While I sometimes still miss the one, I wouldn't want to NOT have these doofuses. They make me laugh; I get some exercise while walking them; they sleep on the bed with me. And I love that they're always glad to see me when I get home! Even if it is because I let them outside to go potty and feed them supper. Still, it's nice to be greeted at the door. :-)
I'm sorry your dog died. That is so hard. Don't do anything until you feel like you know what is right for you. You already know you can't replace your dog. It may just take some time until you are ready to open yourself up to another critter. Wait until you feel a bit more steady.
As a Veterinary Surgeon, and have lost one of my OWN best friends (a cat that I bottle fed and got cancer... I I did chemotherapy, radiation and even amputated his leg... I put a catheter in him when he started to vomit and woke up every two hours to give him injections... It still metastasized to his lungs... I put him in Heaven in my bed myself! It IS so hard, I know! All I can say is let yourself grieve, and it's not replacing, it's saving another that needs love! Rainbow bridge! One of my favorite sayings is "it takes a special person to take the responsibility and kind heart to love something you know you will out live!". God bless and so sorry!