Quoting Alyssa's mommy [EBFT]:" Well thats what I mean, I could put her down to bed now but she will think its a nap and wake up in a ... [snip!] ... around 11-midnight and wake up at 7. I just don't want to throw her schedule off again but would prefer an earlier bed time."
That makes sense.
If she's going to bed at 9pm and waking up at 9am what's the problem?
As my son got older he needed to be awake for 6 hours before his nap, so that would mean waking up at 9am, napping from 3-6pm and then going to bed at 10pm and getting up the next day at 9am and doing the same all over again. That way he was still getting around 14 hours sleep in 24, he was never over tired, always well rested and happy. 1pm might just be too soon for her. I'm in Europe so idk what time it is there, but if she can't stay awake a full day then a later nap sounds like what she needs now. A lot of people seem to be afraid that later naps will mean they go to bed to late and therefore wake up too late the next day. But i've found that a later nap is fine as it means he's had more sleep and so his night time sleep is a bit shorter.
Just try things out and see, try to figure out the awake periods she needs and how many hours sleep she needs during the night to be able to function her best the next day. Sometimes that is a lot more helpful than stressing over clock times