You asked

When will my child begin reading independently?

Every child is unique and will begin reading independently, the best thing you as a parent can do is to let her set her own pace. Be there to lend support, encouragement and praise but understand that every child will learn at a different rate and will respond to different methods of learning.
Spend time reading with her and help her to learn but don’t pressure her. Learning to read can be difficult and isn’t done overnight.
She may begin by simply recognising a word or two, then a few more words and soon she will be putting sentences together. She may begin to start looking through a book with more conviction and concentration. She may be doing very well one day and the next become frustrated.
You should reassure her that she is doing really well and that she will soon get the hang of it. Let her see how enjoyable reading is and how much you enjoy reading.
Even when she starts school and begins to learn to read on her own, you should continue to read to her. The books you choose may get longer and more complex but the simple joy that you both take in reading together will increase and grow.
You can ask your child’s teacher about strategies for helping her to read words that are unfamiliar.  The teacher may advise you to help her find a word within a word, a combination of letters that is familiar or she may suggest using the surrounding pictures as clues to figure out the word.
Your child, at this stage will also be developing interests of her own. You should choose books together that cater to her interests and get her very own library card so she can choose her own books. 

More questions

Getting your child interested in reading is half the battle but you also want to make sure that you are maintaining that interest by choosing the best books.
Reading aloud to your young child is one of the most beneficial things a parent can do for their child.
Giving your child a love of reading is one of the most important gifts a parent can give for their child's education.
Your child is an individual and will begin reading at her own pace. 
Most four year old children are just beginning to understand the concept that letters make words, and words tell a story.
Reading can and should be an exciting and fun-filled time for your child
If you are lucky, your child wants a million books! They love to read and you want to give them every chance to do so. But, as we all know, children’s books can cost a bundle.