If you aren't familiar with Spike and Chester, I recommend you watch from 1:05 - 1:30 before reading on.
Spike the Bulldog and Chester the Terrier are animated cartoon characters from Warner Brothers. Spike is the burly, gray bulldog in the red sweater and brown bowler hat. Chester is the small, jumpy terrier with yellow fur and brown, perky ears.
Because of this cartoon, "to little dog" means to drive someone crazy with inane prattle and constant hanging on. That someone might be a boss, a prospect, a customer, a supplier, anyone in a position to help you. Don't annoy them with Little Dog behavior. Just because it is important to you doesn't mean it's important to them.
For those who remember the movie Tommy Boy, the scene in the diner is a perfect description of Little Dog behavior:
Let me tell you why I suck as a sales man. Let’s say I go into a guy’s office, let’s say he’s even remotely interested in buying something. Well then I get all excited. I’m like Jojo the idiot circus boy with a pretty new pet. Now the pet is my possible sale. Hello there pretty little pet, I love you. And then I stoke it, and I pet it, and I massage it. Hehe I love it, I love my little naughty pet, you’re naughty. And then I take my naughty pet and I go [makes ripping noises] Uuuuuuh. I killed it! I killed my sale. And that’s when I blow it.
Don't be a Little Dog. Stay cool and you will earn respect.