IIWY I would initially just push it later, without cutting. She will already be tired because of the EW, so if you cut the nap too, you will probably just make her overtired.
The reason the nap needs to go later is because early waking is strongly linked to an early nap. If you continue to offer an early nap but cut it short, she will likely get overtired from being up too long between naptime and bedtime. And she will carry on waking early because she can catch up on her night sleep with the early nap.
I would try slowly pushing it towards 12.30/1pm first (which may take a few weeks), then once its been there for a couple of weeks, you will be able to see if
a) her early waking has improved and
b) whether the later nap is having any impact on her bedtime (if she naps at 1pm for 1.5hrs+, she may not be ready for bed at 7pm anymore).
If the EW stops but her bedtime is affected, you can either accept a slightly later bedtime, or if you really don't want a later bedtime, try capping the nap a little.
That is what I tried doing with my DS, but unfortunately he just got really overtired so I had to accept he needs his nap, but this means a later bedtime. Even though I miss the hour of time to myself in the evening, I prefer this to him getting up at 5am.
HTH.x