You asked

How will my baby's eyes develop?

From the very moment your baby is born, her eyes will help her take in the new world around her a little bit at a time. Unlike your baby’s hearing, her sight develops gradually over six to eight months. After this milestone, your baby will be able to see the world almost as well as you.
At birth your baby’s eyes are physically capable of seeing fully but the brain isn’t ready to process all that visual information, so everything is a little fuzzy for a while!
As your baby’s brain develops so too will her ability to see clearly. This will give her the tools she needs to understand and manage her environment.
Your baby will start out only being able to see your face up close when you hold her, but things will become gradually clearer month by month.

More questions

Children's eyes are sensitive so it is vital to protect them from the sun's harmful rays.
Your young child can have their eyes tested even if they can't read
Regular eye exams are essential in order to monitor your child's eyesight.
There are some signs to watch out for if you think your child may have a vision problem. 
Should your child get any kind of chemical in her eye you should treat it as an emergency and bring her to the hospital immediately.
You should take your child to their G.P. or to the hospital if you notice any of these symptoms. 
You should seek immediate medical attention if an object seems to be imbedded in your child's eye. 
If your child appears to have something in his eye you should seek immediate medical attention if it is imbedded in the eye. 
As your baby learns to crawl and begins to explore her surroundings you will need to child proof your house to prevent eye injuries.
Babies and young children are always getting up to all sorts of mischief and eye injuries are quite common. It is important to always consult with your G.P. should any eye injuries occur.