This little scarf took perhaps two hours to knit, but probably less. I knit while watching TV and didn't put much effort or concentration into knitting vs watching. It used under 40 yards of fingering weight yarn on Size 2 needles. I dug out the yarn and pattern while I allowed the part of my River Forest Gansey to block. The hardest part? Translating it!
The original is in French (PDF link). I own an adult version of this sort of scarf in the book 101 Designer One-Skein Wonders but while I could modify that one, it wouldn't give me guidelines for what would fit a doll. The French pattern was already written in doll size and when I debated the difficulty of recalculating gauge (not very hard) AND having to figure out what the "correct" size was for an American Girl doll versus the amusing challenge of translating a language I didn't speak--working with the French pattern won out.
Using fingering weight on size 4 needles:
Cast on two stitches
1st row: knit 1, make 1, knit 1
2nd row: knit 1, make 1, knit until the end of the row
Repeat row 2 until you have 18 stitches
Knit for 10 rows garter
Separate every other stitch onto two different needles. (9 sts on two needles)
Knit 1/1 rib on one needle for 10 rows, break yarn and knit 1/1 rib on other needle for 10 rows
Rejoin by knitting one stitch from each needle, alternating (18 sts)
Knit in garter stitch for 4 inches (20cm)
Halve stitches by k2tog, p2tog, repeat to end
Knit 10 rows 1/1 rib
Next row increase to 18 sts by k1, m1, last stitch kfb
Knit garter for 10 rows
k1, k2tog, knit to end of round
Repeat last row until only 2 stitches are left. Bind off.
I used Size 2 and not Size 4 needles, and Socks that Rock Lightweight yarn (fingering). My "Make 1" was a lifted bar increase, from back to front and then knit into the front to twist. On the first row after joining in yarn, I knit with the live yarn and the tail for several stitches and then just cut the end. It saved weaving in later and doesn't show up at all.