Yes. Check out these opportunities.
Children's Magazines and Ezines
A good place to look is at the magazines you read. Do you see a kid's or children's section? Or there might be a "reader's art" section. Here are some I found:
Amazing Kids! Online Magazine - writing, art, photography or videography, by kids ages of 5 to 18.
chixLIT - by and for girls 13-17 OR chixLITtle for girls 7-12.
Creative Kids Magazine - for kids 8 to 16. "Material may include cartoons, songs, stories between 500 and 1200 words, puzzles, photographs, artwork, games, editorials, poetry, and plays, as well as any other creative work that can fit in the pages of the magazine."
KidPub - books and stories by kids online - free to read, but membership ($12.95) is required to publish stories.
New Moon Girls - writing and art by girls 8 and up.
Stone Soup Magazine - features stories, poems and art by kids 8 to 13
Contests
Contests aimed at children are a good place for young people to submit. Here are a few.
The Young Voices Foundation 2013 contest ends February 28th. This year's theme is: Young Voices of America Speak of Heroes Among Us
Adventure Write Kids has an annual contest for kids under the age of 19.
Creative Communication offers poetry and essay contests for kids ages K-12.
Miss Literati offers writing contests and book giveaways.
National Geographic Kids has some contests - looks as if photos is a consistent contest and others vary.
PBS Kids has a story writing and illustrating contest for kids in K-3rd grade.
Scholastic has an annual Kids Are Authors contest.
Other
Young Authors Guide - this website has advice, links to magazines, and contests ordered by deadline.
The Young Writer's Guide to Getting Published by Kathy Henderson has been a good resource in the past, but the copy on Amazon is pretty dated (2001)
Young Writers Society is an online communities for young writers - ages 13+
Advice
Same as with adults submitting, kids and teens need to follow the directions exactly.


BELLING THE CAT was illustrated by Kwak Jinyoung. Jinyoung did a great job. The mice crack me up. The cat is nice and wicked (from a mouse's point of view). There are two fold out pages and one fold up page, which was a fun surprise. I also like how she did some lettering as if it was cut out fabric.
THE FOX AND THE CRANE was illustrated by Son Junghyun. Junghyun put in lots of details that mean kids could spend a long time reading and rereading before they notice them all. I especially like the image of Fox pulling a trick on Rabbit. Look at the sidewalk and trees in this image. 
If you're heartbroken, don't let it stop you from writing and submitting, at least without great thought. Be encouraged by this guest post by Krista Van Dolzer:
Guest post by Authoress


