Often, beginning writers for young children tend to mix up their short stories versus picture books. It's easy to think that a low word count means PB. In reality, if there isn't enough variation in text to create roughly twenty unique double page spreads, a story isn't a book.
So what do we do with these short stories?
Believe it or not, print magazines still exist. In fact, Highlights for Children has six editors on staff, each looking for different material. Looking for. As in, seeking. As in, go ahead and send off your polished short fiction, articles, how-tos and crafts for ages 6-12.
Simply check out www.highlights.com/contributor-guidelines for more information or join the SCBWI and read editorial wants in the Bulletin.
Additionally, e-magazines exist for kids as well. One such publisher is knowonder! They currently publisher a story a day for kids and parents to share, and have just started accepting chapter book manuscripts. http://www.knowonder.com/
As always, do your due diligence in researching publisher needs, guidelines and reputations.
Best luck in your writing journey~