It does seem like babies tend to make their own schedules around 3 months. It's not a rigid time schedule, but typically wake, 2 hours awake, nap, 2 hours awake, nap, 2 hours awake, nap, 2 hours awake, sleep for night. Seems like most daycares actually help out with that quite a bit because they stay pretty structured.
But most 3 month olds can't stay awake for 3.5 hours. Usually around 2 hours of awake time (sounds like exactly what she is wanting). So she would wake at 6:30, nap at 8:30 (until 10:30?), nap again at 12:30 (until 2:30?), nap again at 4:30 (until 5:30?) and go to bed at 7:30. It sounds like exactly right on track with what you need. Why do you think that's too early?
You're right not to let her get overtired. That just makes it more difficult to sleep! Babies usually don't drop to 2 naps until after 6 months. Either way, the daycare (if that's where she's going) will probably just mold her schedule to fit theirs. But 3 naps is right on track for a baby her age. :)
A couple of resources for you:
Sleep chart (because it's hard to know how much sleep babies need): http://www.parenting.com/article/Baby/Care/Baby-Sleep-Chart
http://www.babycenter.com/0_baby-sleep-basics-3-to-6-mont...