Here you go gardenway--if you are making it for a 1 year old make it 16 to 19 inches around depending on the childs head size. Some kids have bigger heads than others. You can Measure the childs head around to get a better idea of his head size

HEAD SIZE CHART

PremieÂ5 lbs-------------------------------------------------------------------------
HAT AROUND---11-12 inches-------Hat height------ 5- 5 ½ inches

Newborn-------------------------------------------------------------------------------
Hat around------12.-13. inches-----Hat height-------5 ½ -6 inches

Baby 3-6 months ---------------------------------------------------------------------
Hat around------14-15 inches-------Hat height------ 6-7 inches

Baby 6-12 months----------------------------------------------------------------------
Hat around------16-19 inches------Hat height-------7.5 inches

oilpainter - thanks for the info.
The problem is I can't measure the child's head. She lives out of state. I guess I could make one or more circumference of the same hat and hope one of them fits! I'll see her at Christmas. (or I suppose ask the mom to measure for me).
She is wearing 9 mo. in clothes but 12 mo. suggested for/by Christmas.
Also thinking of making a scarf to go w/hat - any thoughts on 26" being a good length?

If you make your hat with lots of ribbing, that'd help..and, I always knit with wool...then I can block it to a size I want, and the baby's mother could do the same....I often, using push pins, stick a small project like this to the back of the guestroom door...pinned the size I want it....spray it with water and leave till dry...presto...the size I want!
As far as the scarf length goes, if I were you I'd do a google and find out the average height of a one year old, and from that, figure the length that would be appropriate.

To each his own sandra but I never knit with wool. I can't stand the feel of it, it's prickly to wear and shrinks if you happen to put it in the dryer.

gardenway:

What kind of hat are you making. If it's a toque do it in k1-p1 ribbing and it will stretch. With the toque with earlugs pattern that I offered The newborn size of 13.5 inches stretched to 20 inches, because it was done in ribbing

sandra and oilpainter - good suggestion to use ribbing. I've already made a hat, crocheted. It is beanie style. Starts out as dc (top circle) and then the balance is a textured stitch, ending with a band of 3 rows of sc. I'm pleased with how it worked up. I used "I Love This Yarn" (Hobby Lobby). However, I think I will also make another one using the next size bigger hook. If neither fits, then some charity will be getting two nice hats. I also can consider making a third hat in knitted ribbing!!