It sounds to me like you've just got a night owl and you're putting her to bed too early. She is getting a TON of sleep. 13 hours at night is a very long time especially when combined with a 3 hour nap. Normal for this age is 12 hours TOTAL sleep between night and day. Most agree that getting a kid to sleep 12 hours at night is pretty incredible, most sleep between 10 and 11 at night. Congrats on having a baby that sleeps till 9AM, I'm totally jealous. If she's sleeping through the night till 9AM, try pushing the bed time back to 9PM. keep it there for one week and if still having issues try 9:30pm.
Also, you should do a very consistent and calming night time routine inside her bedroom, not outside. I really think your problem is just a too early bedtime though, she's simply not tired yet because she's had SO MUCH sleep at that point. I think once she's more tired it won't seem like play time. Here is what Ferber says - no TV before bed, and no energetic play (tickles, chasing around the house, running games, etc) an hour before bed. Don't make the bedtime routine too long (common mistake) 30 minutes is how long it should take. It doesn't really matter what you do as long as it is calming, consistent and ends inside her room, but most people start with a bath, then maybe saying good night to daddy or the dog or whatever, then pajamas inside her room, then never leave the room, turn down the lights (a good sleep signal), and the read books calmly in her bed or rocking chair, sing quiet calming songs, etc. What matters most is that it is the same order every single night. You are giving her a countdown to going to sleep. As she gets used to it she will get sleepy at the end of the routine (provided she is reasonably tired) Again, I really think you're just putting her to bed too early based on when she wakes up. If she does 12 hours at night and 2 hours in the day she's already 2 hours ahead of normal for sleep (which is great) but you can't reasonably hope for more than that. 9PM should be earliest bed time, but could even be as late as 10 if she keeps waking up at 9AM, sleeps through the night and keeps up those long naps.