Okay, so I just got a free copy of Dagger, Supplemental Rules for Classic Role-playing with Kids by Brave Halfling Press for entering Erik Tenkar's OSR Superstar contest over at Tenkar's Tavers. The rules are a 14-page pdf of which 7 pages are the actual rules--and in this case the low ratio of pages with stuff vs. pages without stuff is very good news.
Dagger takes the already fairly simple OD&D rules and simplifies them down even further. It's really all you need to get started--but note that it is a supplement and not a complete stand-along rules set. It is designed to make character creation and play easy and assumes the DM is already generally familiar with OD&D. For instance, there are no ability scores! The major things missing from Dagger which you'll need to bring in from elsewhere are equipment lists, treasure tables, and magic items.
I think this set of rules accomplishes what it sets out to do and it would work not only as rules for young kids but older "kids" as well.