Aww, of course. I don't tend to work to patterns to be honest but for a simple now faff hat (just a simple beanie with a fold up so it's adjustable) I use soft baby double-knit, cat on size 5 needles (nice stretch then for comfort and accomodating growth) though size 4 will give a more compact knit.
I cast on 20 stiches for a turnup though you can alter as appropriate then do a simple knit pattern for as many rows as appropriate (knitting the hat sideways if that makes sense) then gather by threading through and pulling in at the top (so less stitching to form anything aggravating at the top) and join the side seam.
Very quick to do and you can change as apropriate. I tend to keep it simple for tiny ones. Striped ones look lovely.
The one I did last night is little, 9 inches wide and 4.5 inches up (then turned up so not so high.
For sizes, I have this handy as it goes by weight so good for premature babies.
http://www.bevscountrycottage.com/size-chart.html