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What does her schedule look like now?!

No tips other than do what works. Her schedule is similar to DS's. He's 13 months and has always woken up between 4-6 am and I have to nurse back to sleep. His afternoon nap is his longest but he's been waking up an hour in and I cuddle on the couch till he falls back asleep (I'm abusing this b/c he's usually in daycare and I love the extra cuddles!).
I'm not sure if anything you do will fix it?

I'd do whatever it takes to get her the most sleep and wait it out. She will resolve it on her own.

Everything @gingerbebe: said about not going in unless LO is truly upset. We still do that at 15 months. I always want him to be in his crib for at least 1.5 hours. So if he wakes at the 1 hour mark, unless he's actively crying and clearly upset, I leave him.
That being said...for the 5am wakeup we had to do CIO. It was recommended by my pediatrician at 4 months. Honestly it only took 3 days for him to stop waking and to sleep 6:30-6:30! I know it's not for everyone but that is how we got rid of that 5am wakeup in a very short amount of time.
Oh and I remember reading about the 5am wakeup on babywise as well. It's mostly talking about it as a feeding but it still has a few options you could maybe apply. Obviously we did the 5th option
http://www.babywisemom.com/2013/07/5-6-am-night-wakings.html?m=1

And I again just want to echo what gingerbebe said: if she is waking happy at 5am JUST LEAVE HER! You may be surprised and she may just got back to sleep. I have a "real life" friend who has a 15 month old like me. She had been going in the second he made a sound at 6am. I finally said "look if he's not crying just leave him and see what happens". She emailed me the next day and said she left him and after 20 mins he went back to sleep till 7:30! And now he sleeps till 7:30 every day.

As for naps and waking at 30 mins, she's definitely old enough to connect sleep cycles. and I think she was doing that before? So I hate to say it but maybe a new habit was formed. Like she woke up at the 30 min mark a couple times as coincidence and since you went in she now wants/expects it? It's also possible it's developmental (like maybe she just started or is about to start crawling for example). I honestly would again just leave her if she's waking happy. She will eventually learn that tou aren't coming in and go to sleep till nap time is over. Even when she doesn't go back to sleep, it's still good for them to be alone in a quiet dark room as part of the nap time than to go in and disrupt it.

My last thought is that I would shorten wake times. At that age we weren't even on 2-3-4 yet. We were on more like 2-2-3 or something like that. I would try that. It's possible that because she is waking during naps now she is overtired. Overtired babies not only have a hard time falling asleep but also staying asleep. So maybe before CIO for naps or anything else, try that. Shortening wake time is relatively easy and you'll know pretty quickly if it works. It might take a few days to see the positive effects but be consistent! It may mean some EARLY bedtimes for a while. Trust me it is worth it! I have a friend who is a sleep consultant and she calls it "crazy stupid early bedtime" but it's necessary for some babies while they adjust their schedules.
I always find wake time to be a delicate balance. I posted here a few weeks ago that my sons perfect naps had gone to hell and maybe it was time for 1 nap. But once I adjusted his awake time he is back to two 1.5-2 hour naps a day with a slightly later bedtime ( 7/7:30 instead of 6/6:30). It's working beautifully! So my point is it took some trial and error and a lot of patience but some kids are super sensitive to even MINUTES difference in wake time!

Good luck! Feel free to wall me any time