My three month old doesn't nap consistently and the length varies every day. I've had a good routine going but napping isn't going as planned.

The schedule looks like this....He wakes and eats at 7:00am and nap starts at 8:30, eats at 10, naps at 12, eats at 2, naps at 4, eats at 6, cat nap at 8, eat at 9 and down for the night. He will sleep the entire night but his napping during the day may be 15 minutes here, 30 min the next and maybe an hour if I'm lucky. I've read they should nap for 1.5 to 2.5 hrs. three times a day equaling 15 hrs plus nighttime. He's been so fussy and shows signs of overtired but won't sleep....

Should I put him down to bed earlier so he gets more sleep? He's getting 9.5 hrs a night.

Will it effect my milk supply if I go longer than 9.5 hrs without nursing ?