No, not normal. Make sure she has plenty of fresh, clean water, layer feed and free choice access to oyster shell. If she continues to lay eggs like this you should probably give her calcium orally and de-worm her with Safeguard or Valbazen.
I have seen an egg like that in my 2 year old salmon faverolle about the same time she stopped laying 4 months ago. It looked to me like either a membrane on the outside or mineral deposits. It washes off under warm water. Since it is a new pullet, she may just be having some kinks in her egg production. Here is a good BYC article on egg problems: https://www.backyardchickens.com/a/common-egg-quality-problemsI have a
new pullet that laid an egg with a thick coating on it, almost looks like a layer of skin
Hens go broody when you don’t want them to… and won’t go broody when you do. 
