N.O.
WOW, you basically just said what my 3 mnths old schedule is like. He was born April 1st and has been the best little baby. He's sleeping pretty good through the night, wakes up to feed at night and goes right back to sleep. When he's awake during the day it's usually about an hour to two and then naps for about 45 minutes to an hour.
He sleeps alot during the day in his swing and is also exclusively breastfed and usually he ends up in the bed with me at night.
You sound like you're doing everything right. They don't typically have a set "schedule" until about 6 mnths old and even then it can be off at times.
Keep up the good work and congratulations on your new baby girl! : )