X2Sometimes when they lay, especially if it's a large egg, they can break a small blood vessel, and it's nothing to worry about. Since she's a new layer, I wouldn't worry too much about it, it will probably work itself out as she gets her laying parts regulated. It can happen occasionally to any laying bird and unless there are copious amounts of blood it is not something to worry about.
As far as the egg song goes, some birds are quite vocal every time, some are quiet most of the time, and you just never know. As she's low in the pecking order she's maybe thinking discretion is the safe way to go. Given time she may start doing the egg song, or not, you'll just have to see.
Images like this show just how vessel rich the repro tract is and just how easily a small rupture could occur