If you want to use your own pattern/create your own pattern, a good hat size that I've been using is 6 in tall for a hat, excluding a rolled brim (this means that if your hat has a rolled brim, roll it back down and measure it up). As for diameter, I don't really have much to say. The main pattern I've been using calls for 65 stitches on Size 8 US Circs to make a child-sized hat, so maybe use that number to help size your hat. If you need any more info, just contact me and I'll help. Again, with the wide age spread, basically any hat will do!
This is a WIP List, by the way!
EASY PATTERNS (basics--knit, purl, decrease)
Sprial Brim Hat (VERY easy--it's the basic pattern I've been using. I can get one of these hats done in less than three hours with very little yarn and very little thinking! I would choose this if you're low on time or want to use up some extra yarn.)
Rolled Sprial Brim Hat (takes a little more thinking, but will go quick because of bulky yarn. It is already sized for children, too.)
Rolled Brim Hat (even easier than the others, but must resize for children.)
Striped Hat (just knitting and purling, but the pattern makes it look unique!)
HARD PATTERNS (cables, embellishments, etc.)
I searched through all the archives of Knitty.com and chose the hats that I think would be suitable for this project. All might need to be adjusted for size, as many are meant for adults but could also work for children as well. I also put all links from Knitty under the "Hard Patterns" category because, well, they all look intiminating!
Knitty Winter 07--Toasty Topper
Knitty Winter 07--Bloody Stupid Johnson
Knitty Fall 05--Astrodome
Knitty Winter 06--Center Square
Knitty Winter 03--Coronet
Knitty Winter 04--Cross Country
Knitty Summer 06--Crosspatch (this one looks very Tibet-ish to me!)
Knitty Fall 02--Double Knit Hat
Knitty Winter 03--Flappers (felted, so feltable yarn would be needed)
Knitty Winter 06--Hexed
Knitty Fall 07--Intarsia Fun
Knitty Summer 06--Klein Bottle Hat
Knitty Winter 04--Peruvian
Knitty Summer 06--Sock Monkey Hat (very cute and kid-appropriate!)
Knitty Winter 05--Real Stocking Hat
Knitty Fall 06--Sugar on Snow
Knitty Summer 06--Swell
Knitty Summer 06--Tychus
Knitty Fall 02--Vinter Lue
