Yeah, but again, it's not like she's the only one who's gone through hard times or had responsibilities; she's just the only one who whines about it. Sokka was faced with responsibility at a young age, too. His father left when he was rather young (maybe about ten or eleven?), leaving him to be one of the last defenders of the entire tribe, and Sokka was left to train the children of the tribe how to battle.
I don't really know WHY they left their entire village unprotected when they knew the Fire Nation liked to come down and kick them around every so often, or why they didn't just relocate to where the Fire Nation might not find them for a while, but it doesn't matter. Sokka was left with the burden of protecting his homeland, knowing that if the Fire Nation ever came back, he would be their last defense; he would have to fight back an entire army, and if he failed, everyone and everything he knows would perish.
To me, that's a lot harder to deal with than just caring for the family. This is about defending your entire tribe; many families depending on whether or not you are strong enough to protect them when the time comes to fight to the end. But Sokka still knows what fun is.
What about Aang? At a young age, he was also dealt a heavy blow; he's the AVATAR. He has the entire weight of the WORLD on his shoulders. You can argue whether or not he understands the gravity of the situation, but I think Azula "zapped" some sense into him to see what's at stake. He still makes time to have fun.
Willing to argue that she doesn't have fun because she's had a great loss? Well, Sokka shares her loss, plus he's lost a girl he loved, Yue. Aang has lost his entire nation; everyone and everything he knew is gone. Toph never really had anything, no friends to speak of and what appears to be an emotionally distant family. You'd think this would be more emotionally crippling than having several loved ones and then losing one of them, because at least Katara still had her grandmother and brother who cared. Toph has hardly ever been shown true affection from her parents or friends. But she still has fun.
We're supposed to feel sympathy for Katara, because she's never known any fun; she's a surrogate mother to her family and she's never been able to be a kid. It's so sad how she's had responsibilties and losses. Well, so has everyone else in the Aang-Gang, and they don't seem to be hurting for fun. Why are we supposed to feel sympathy again?