There are two competing visions in the ebook world: the embedded font vision (pushed by Adobe) where ebooks creators are expected to choose interesting fonts and embed them (generally by using Adobe InDesign).
The other vision is using the system fonts provided by the reading system/device and letting the readers decide.
Technically the early devices and reading systems have not supported embedded fonts uniformly. (It differs according to the font and the actual device). Support has improved over the years, but it still requires lots of testing.
Fortunately reading systems have increased the number of fonts already available. Fonts on apple iBooks are pretty great, and Amazon included a great font Bookerly on their Kindle devices a few years ago (which was a pretty big deal).
I guess with poetry it makes sense to choose custom fonts, but be prepared for the possibility that some reading systems won't display them or the reader may simply turn the publisher defaults off. I've encountered a lot of problems on the lesser known ebook readers on android.
I might change my way of doing this soon if rendering of embedded fonts is more reliable, but my rule of thumb has been NOT to specify a body and p font and then specifying a headline font found on the reading system in css and embedding font in special cases. Also, I sometimes use a different font for title page stuff.
Here's some good reference info:
About Georgia, of course it's a great font, but did you realize that Google Play Books doesn't include it as a system font -- which is really bonkers.
Finally, I wish there was a font foundry which in addition to selling licenses for ebook production could guarantee correct rendering on the major ebook reading systems.