Maybe it's just me, but I actually think that if MacFarlane continues to produce more Family Guy episodes and seasons that it will be just fine without Brian.

It will be a little said that one of their primary Show-tune performers will be gone (leaving it to Peter and Stewie to sing and dance), however the overall dynamic of the show will not be affected save for Stewie's character, which they actually did address in the episode of Brian's death.

I think that perhaps Seth should have split Brian's death and the adoption of Vinny into two different episodes, but it also does go to show that the family, while they respected and loved Brian, saw him as more of a loyal family pet than a person with his own goals and aspirations. Remember, Meg and Chris are both teenagers so they would handle Brian's death more maturely than baby Stewie, who was by far the most devastated. It's one of the rare points of the show where emotions are actually fairly realistic given each character's age.

Now, why do I think Vinny works as a character? Well, he does have a pretty over-the-top personality and accent,k you probably couldn't make him any more Italian mobster unless you gave him the prefix "cousin" and had him work for the Godfather, but that works for his character, because lets face it, a bipedal talking dog is a pretty ridiculous concept, let alone having gone to college and working as a radio personality. I think it will be a good fresh start to have a character we aren't required to take nearly as seriously like we were expected to take Brian's character.

Speaking of that, I'm going to briefly touch on Fanfiction Tropes. Specifically, what Brian's character represents. Brian is pretty much the "Marty Stu" of the show. He represents Seth MacFarlane as an avatar within the show. Simply, Brian is Seth MacFarlane's attempt to insert himself into the Family Guy world. It's not so hard to believe, as some of us remember the lawsuit someone filed against Seth MacFarlane, which turned out to be a real-life neighbor of Seth's that he based Peter's character on.