Haha I love the cartoon Avril I think they were just going for a general punky look, she was famous for the pink hair in TBDT era and then they stuck it with her famous raccoon eyes and a black top with the LG star. I think the point is that it's supposed to be a bit parody-like, so that people can easily recognize it's supposed to be Avril Lavigne.
For those who plays the game (and a fun fact for us that don't )
•Avril Lavigne is the first performer in the lineup. But first, you need to unlock her. Kick it off by repairing her chic seating arrangement, then collect glowsticks, guitar picks and hockey pucks from around town. The hockey pucks are rare, so if you have Lois, Herbert and Bruce unlocked, this will go a lot faster! Avril unlocks much of PeterPalooza’s new content, so she’s a good character to focus on first, along with Rockstar Peter.
"The great thing about Lavigne's songwriting is that it always conveys a deeper meaning without overreaching or busting out the thesaurus.The piano driven "Hush Hush" emits a rush of feelings - regret, anger, desperation, nakedness and finally, faint hopefulness - and unpacks them tidily presenting as Lavigne as a pop artist one can trust to handle the job." - Billboard
My friend has the game and even though he hasn't unlocked Avril yet, he says that apparently all the celebs featured in the game lent their voices and said some lines for their characters. He said one of the things Avril says is something like "My hair is like a mood ring!" And I guess one of the objectives is that you need to get Avril to play a concert and one of the things you need to do is fly a banner with her logo on it.