my sister is 11 years old and she just started watching anime are there any animes she could watch.

Hetalia: Axis Powers

Free! Iwatobi Swim Club/Free! Eternal Summer

One Piece

Naruto/Naruto Shippūden

Ouran Highschool Host Club

Puella Magi Madoka Magica

Sword Art Online

K-ON!!

Lucky Star

Sailor Moon

Pokèmon

Fairy Tail

Noragami/Noragami Aragoto

Mermaid Melody

Kuroko no Basuke

Haikyuu!!

Magi: The Labyrinth of Magic/Magi: The Kingdom of Magic

La Corda d'Oro Primo Passo/La Corda d'Oro Secondary Passo

Dragonball/Dragonball Z

*whispers* digimon tamers
and PLEASE don't look down on it because it has "digimon" in it's name, don't.

Tsubasa Chronicle

The Devil is a Part-Timer! [pictured]

His and Her Circumstances (if she likes romance)

pag-ibig Live!

Binan Koukou Chikyuu Bouei-bu LOVE!

Tsuritama

Assassination Classroom (not as bad as the name sounds, I promise)

Pokemon
Lucky Star
my opinion here but Melancholy of Haruhi Suzumiya

and Sailor moon

Sailor Moon
Lucky Star
Cardcaptor Sakura
Fruits Basket
Kaichou wa Maid-Sama
Pichi Pichi Pitch (Mermaid Melody)
Special A
Soul Eater Not!
Uninhabited Planet Survive
Zero no Tsukaima
Anohanna
Kaleido Star
Kyou Kara Maou!
marmelada Boy
Baka to Test to Shoukanjuu
Princess Tutu
Sakurasou no Pet na Kanojo
Super GALS! Kotobuki Ran
Tokyo Mew Mew
Ultra Maniac

definitely:
Digimon
Shugo chara! (most recommended)
Kirarin Revolution (also one of the good choices)
Yumeiro patissiere
Tokyo mew mew
Kaleido bituin (my childhood)
Nana
Chobits
Dragon Crisis!
Rozen Maiden
Fairy tail/Naruto/Bleach
Shaman King
Death note
Hetalia
No Game No Life

Digimon

Pokemon

You-Gi-Oh!

Totally Spies

Naruto

One piece

Lucky Star

Sailor Moon

InuYasha

Dragon Ball

Sword Art Online

Sailor Moon

Fullmetal Alchemist

Shaman King

K-On!

(Couple of Episodes of) Fairy Tail

These are all PG- 13:
Akagami no Shirayukihime - Drama, Fantasy, Romance, Shoujo
Akatsuki no Yona - Action, Adventure, Comedy, Fantasy, Romance, Shoujo
Ano Hi Mita Hana no Namae wo Bokutachi wa Mada Shiranai - Drama, Slice of Life, Supernatural
Ao no Kanata no Four Rhythm - Drama, School, Sci - Fi, Sports
Barakamon - Comedy, Slice of Life
Black Rock Shooter - Action, Drama, School, Slice of Life
charlotte - Drama, School, Super Power
Chuunibyou demo Koi ga Shitai - Comedy, Drama, Romance, School, Slice of Life
Denpa Onna to Seishun Otoko - Comedy, Sci - Fi, Seinen, Slice of Life
Fairy Tail - Action, Adventure, Comedy, Fantasy, Magic, Shounen
Hataraku Maou-sama! - Comedy, Demons, Fantasy, Romance, Shounen
Hidan no Aria - Action, Comedy, Romance, School
Hiiro no Kakera - Fantasy, Romance, Shoujo, Supernatural
Himouto! Umaru-chan - Comedy, School, Slice of Life
Hyouka - Mystery, School, Slice of Life
Inu x Boku SS - Comedy, Romance, Shounen, Supernatural
Isshukan mga kaibigan - Comefy, School, Shounen, Slice of Life
K-ON! - Comedy, Music dcool, Slice of Life
Kono Subarashi Sekai ni Shukufuku wo - Adventure, Comedy, Fantasy, Supernatural
Kuroko no Basket - Comedy, School, Shounen, Sports
Kyoukai no Kanata - Fantasy, Slice of Life, Supernatural
pag-ibig Live! School Idol Project - Music, School, Slice of Life
Lucky bituin - Comedy, Parody, School, Slice of Life
Maoyuu Moau Yuusha - Adventure, Demons, Fantasy, Romance
Mekakucity Actors - Comedy, Romance, Sci - Fi, Super Power, Supernatural
Mikagura Gakuen Kumikyoku - Action, Comedy, School
Mikakunin de Shinkoukei - Comedy, Romance, School, Slice of Life
Mondaiji-tachi ga Isekai kara Kuru Sou deso yo? - Comedy, Fantasy, Supernatural
Nagi no Asukara - Drama, Fantasy, Romance
Naruto - Action, Comedy, Martial Arts, Shounen, Super Power
Nichijou - Comedy, School, Slice of Life
No Game No Life - Adventure, Comedy, Ecchi, Fantasy, Game, Supernatural
Non Non Biyori - Comedy, School, Shounen, Slice of Life
Plastic Memories - Drama, Romance, Sci - Fi
Sakurasou no Pet na Kanojo - Comedy, Drama, Romance, School, Slice of Life
Shigatsu wa Kimi no Uso - Drama, Music, Romance, School, Shounen
Shokugeki no Souma - Ecchi, School, Shounen
Steins;Gate - Sci - Fi, Thriller
Suisei no Gargantia - Action, Adventure, Mecha, Sci - Fi
Tamako Market - Comedy, Slice of Life
The Idolm@ster - Comedy, Drama, Music
Toradora! - Comedy, Romance, School, Slice of Life
Watashi ga Motenai no wa Dou Kagaetemo Omaera ga Warui! - Comedy, School, Shounen, Slice of Life
World Trigger - Action, School, Sci - Fi, Slice of Life, Supernatural
Yahari Ore no Seishun pag-ibig Comedy wa Machigatteiru - Comedy, Romance, School
Zetsuen no Tempest - Action, Drama, Fantasy, Magic, Mystery, Psychological, Shounen

Cardcaptor Sakura
Shugo Chara
Lucky Star
AnoHana
Nagi no Asukara
Fairy Tail
Pokemon
Yu-gi-oh!
Digimon
Fresh Precure!
PriPara
Ano Natsu de Matteru
Sailor Moon
Asatte no Houkou
Busou Shinki
Chuunibyou demo Koi ga Shitai!
Hyouka
Comet Lucifer
Detective Conan
Tokyo Mew Mew
Jewelpet Twinkle
Mai-HIME
Spice and lobo
Ao no Kanata no Four Rhythm
Musaigen no Phantom World
Usagi Drop
Your Lie in April
Full moon wo sagashite
Mermaid Melody
Shougeki no Souma
Amnesia
Doraemon
Yumeiro Patissiere
Hikaru no Go
Princess Tutu
Angelic Layer
Kobato
Chuunibyou demo Koi ga Shitai!

If you want her to watch a short anime, than I suggest Lucky Star. For something a bit longer, Soul Eater. If you want a long anime, than I suggest One Piece or Naruto.

Mew mew power
Shugo chara
Pri para
Yumerio patissier
Nagi no asukara
Aikatsu
Jewelpet tinkle
Lady Jewelpet