Hi there Barn Yarn Chicken
Congratulations on the first egg!
Chickens new to laying can sometimes take a while to get the hang of it and their internal plumbing can also need some adjustment time.
She may not have broken the egg intentionally to eat it and could have laid it standing up or accidentally squashed it.
If chickens come across a broken egg, they are opportunists and will most likely eat it but they are not necessarily eggs eaters per say. My gals will eat a broken egg but have never broken one intentionally to eat it.
With it being her first, the shell may not have been very hard and this could also be the reason it broke.
You mention that you have oyster shell on hand which I recommend keeping separate [away from their food], in the coop etc where they can partake if and when they desire. I find my gals normally have a peck before going to roost at night.
Having said all that, there are chickens who are egg eaters and if you are concerned that you have an egg eater, there are numerous threads on the topic. If you pop 'egg eating' into the Search option, you will be able to find them.
Good luck!