If an egg is broken, about any chicken will eat it. I dont consider that an egg-eater. To me, an egg eater is one that purposely opens a good egg to eat it.
I had one of those once, a Delaware I had been planning on keeping. She would open a couple of eggs a day and some of her buddies would help her eat them. It took a while to figure out which one was opening them. As soon as I figured out which one it was, she went to the crock pot. The problems were over. She had not yet taught her buddies to open a good egg.
What probably happened is that the pullet dropped an egg accidently. It was very thin shelled and it broke. Chickens did what chickens do and ate it. It is not at all unusual for a pullet to just drop her first egg wherever she is, on the roost, in the coop or run, wherever and whenever. Some of them just take a while to learn control.
Its also not at all unusual for a pullet to lay a strange egg at first. Sometimes you get soft or no shelled eggs. Quite often you get eggs with a real hard shell. Thats pretty normal. The egg is usually small and the shell gland makes enough shell material for a full sized egg. Those little ones can be real hard. You might get a yolkless egg, an egg with no yolk, or a double yolked egg. If these things happen, the pullet usually debugs her internal laying factory in just a few tries, certainly within two weeks.
With everything that has to happen, its pretty amazing to me that most pullets get it right the first time, laying a good egg in a nest.
I fully agree to get oyster shell and offer it on the side. Hens usually instinctively know they need the extra calcium for their egg shells. I would not mix it with the feed. The others arent laying yet. They dont need it. It may be that the pullet that laid the egg wasnt eating enough calcium or it may be that her shell gland still had some kinks in it. Give her time.
I also strongly believe in keeping a fake egg in the nest even if they are used to laying in those nests. It shows them where to lay. I use golf balls. I had a fake egg get scratched out of a nest because the lip was too low. It landed right in front of the nest. A hen laid an egg right beside that golf ball. When I fixed the low lip and put the golf ball back in the nest, she laid her next egg where she should.
Right now I would get the nests ready and make the oyster shell available, but I would not panic. Definitely observe them for any problems, but dont be shocked if things work out.