Not the first time they’ve taken a nasty shot at her. Remember the episode that aired just before the election when Stewie found a McCain/Palin button on his Nazi uniform?
Serious question: Does this even qualify as a joke? There’s no punchline per se; the humor, such as it is, lies in knowing that (a) the character has Down’s syndrome, (b) Palin’s son also has Down’s, and (c) Palin is a former governor of Alaska. The goof, I guess, is that … all Alaska governors have kids with Down’s? Or that all of Palin’s kids have Down’s? (They don’t.) Whichever it is, consider this a useful illustration of the notorious laziness of the FG writing staff, beautifully mocked by “South Park” a few years ago. Looks like the manatees only delivered one ball for this joke.