I'm making the sock up as I go along, but the pattern is Garter Rib from Sensational Knitted Socks; by Charlene Schurch. I used it for my Lullaby Socks recently. Here's my progress:
I plan on weighing the sock when I get done. Then I will know which of my leftovers from adult socks are enough for a pair for DGD2. Quick and easy sock fun! I'm so lucky to have a little girl to make socks for! (A little boy would be OK, too!)
I should point out that I'm writing the pattern as I go. Once I finish the second sock, I will know if I can understand my own pattern. Then I'll make it available for free. It's the right size for a size 6 child's shoe, which our 16-month-old DGD will be in after she outgrows her 5s.
Thank you, thank you (in advance) for making the pattern available. My DGD is just 18 months & I am having a difficult time finding patterns or directions for proper sizing for her socks. So far I cheated & only make tube socks :(
Charlene Schurch's Sensational Knitted Socks and More Sensational Knitted Socks have children's sizes equivalent to a size 4 shoe and up. You can make any sock in pretty much any size. I went to a 44 st CO because I didn't want to change my needle size, so I had to make some adaptations to the pattern. They are good books to work from. Pretty soon you can pretty much wing it.
The first book is here: http://www.knitpicks.com/cfbooks/book_display.cfm?ID=30656
Looks like they don't have the second book right now.
It might now be as detailed or go down as to that small, but Ann Budd's The Knitter's Handy Book of Patterns contains children's sizes for socks. Also you can find a chart here for shoe sizes. It doesn't really give width but it does give length which might be helpful.
I guess the size in inches is length, not circumference. Because they sell shoes, I'm thinking probably foot length, as you say. Both are important, though, for socks. Charlene Schurch's books list shoe size, circumference of foot, recommended height of leg, heel flap, heel to start of toe, toe length and total foot. That information and your gauge is pretty much all you need to wing it.