Reddit reviews What I Like About Me!: A Book Celebrating Differences

The only book I can think of is called Don't Cry, Big Bird BUT I would ask you to preview it to see if you think it's acceptable because I don't remember all the details and I don't want to be held responsible for traumatizing your cousin!
From what I can remember, it's a picture book where Big Bird is very sad because he's too tall to join in games (jump ropes are too short, etc.). He's all sad about it, but then Mr. Snuffleupagus, who is also really big, says that he likes Big Bird's size. He helps Big Bird modify games (tying two jump ropes together) and eventually Big Bird likes his size and finds it useful-- he rescues his friend's kite from a tree when no one else can.
The reasons I can remember for not recommending this book wholeheartedly-- I believe they use the word "big" instead of "tall." It seems like a little thing, but for a girl who is already feeling self-conscious, it might not be the best choice of words. (And yes, no one should be ashamed of their body, regardless-- but I know that personally, when I was called "big" as an underweight but tall preteen, it stung.)

Another resource-- not specifically for tall girls, but adhering to the theme of loving yourself for who you are-- I found this list of "Positive Princess" books really helpful when I started nannying for a very appearances-centered kindergartener. She loves princess books, but a lot of them weren't sending a very positive message. These princess books focus more on having a healthy view of yourself rather than idolizing some airbrushed "Princess" character. I haven't read all of these, but Jane Yolen's and Heidi Stemple's Not All Princesses Dress in Pink is phenomenal.

More awesome picture books celebrating differences and diversity (Amazon has most of these for less than $3 used, and they're mostly popular enough that I would think your library would have them):
It's Okay to be Different
What I Like About Me
I Like Myself!

To take a different approach-- I know this sounds shallow, but when I was still growing and way more self-conscious about my height, I LOVED the fact that Nicole Kidman was (well, is) 5'11" (I was obsessed with Moulin Rouge). I ordinarily do not care about celebrity...stuff, but I thought it was so awesome that she was the same height as I was! Depending on what your cousin's interested in, consider showing her some pictures of tall girls to boost her confidence. For example, if she's familiar with the President's family, Michelle, Malia, and Sasha Obama are all quite tall (Michelle and Malia are both 5'11", and Malia's only 14!) The Obama girls are gorgeous and stylin, and I know I would have loved to see photos of tall younger girls when I was a kid (as opposed to tall women). Hell yeah, tall first family!
5 is too young for The Hunger Games, but Jennifer Lawrence is 5'9 and taller than her costar. She also seems to have a fairly positive view of health/body image as well.
There are a lot of tall women in the media-- Queen Latifah and Tyra Banks are 5'10, Taylor Swift (if she's into her music) and Karen Gillan (I love Doctor Who too much to not include her) are 5'11... and that's just a start! Look at Olympic athletes (Missy Franklin is only 18, 6'1, and a 4-time gold medalist) for other tall role models!

But at the end of the day, more than any books or media, you are the one who will have the most positive impact on your cousin! Make sure to talk about your own height in a positive manner, don't set a bad example by saying anything negative about your own body (or anyone else's), and be sure to mention how much you like being tall when you're around your cousin. I outgrew my mom, sister, aunts, uncles, and all my male and female cousins as a kid-- I would have loved to have a role model like you! Your own personal relationship with your cousin will be by far the most powerful and long-lasting influence on her self image.