pullet just means a female chicken under a year of age. Once they start laying they've reached reprodutive maturity and can lay eggs and have chicks (if their eggs are fertilized and they go broody to hatch the eggs)
Having had a lot of experience with hatching, I would suggest waiting on hatching eggs from young layers as their eggs tend to be smaller than what they will eventually get to be. Smaller eggs tends to produce smaller and less healthy chicks. That being said, if the eggs are of normal size and you have let them get through at least two to three weeks of laying, they should be okay.
Pullet is a termed used to describe a female chicken under 1 year of age. Normally, you would want your pullets to settle into their laying pattern before you start pulling eggs to incubate. And, a pullet isn't normally going to hit their peak production prior to a year old anyways.
In this other post, you said you read it in "Storey's guide to raising chickens" not "My grandpa told me pullets don't reproduce well"...