Is there a particular type of dog your son likes? Is he a Clifford fan, or likes Tin Tin's dog... or just any dog in general?
Will there be different ages of kids there, or mostly adults? Would you do any party games with older kids?http://allrecipes.com/recipe/puppy-chow-i/
this is a snack called Puppy Chow, its pretty easy to make but I'll admit I never tried it
You could make Rice Krispy treats in regular and/or cocoa crispies and mold them into little bone shapes.
Using a bone shaped cookie cutter, cut out little sandwiches. The cake could be a big "bowl of dog food".... round cake, frosted, decorate side with baby's name and paw prints, and cover top with cocoa puffs.
For games, you could do "pin the bone in the doggy's mouth".
Gift bags could include a little dog plushie or stuffy, and maybe a chocolate or white chocolate dog lollipop (there are molds to make these). Stickers or fake tattoos might be fun.
For the grown-ups, you could frame little pics of the baby, using $1 store frames. Make sure he's wearing an "I'm One" themed something, so its really a keepsake.