I am the mother of two boys who learned to read at 4, and a preschool teacher who has at least a few 4 year olds learn to read each year, and I agree with everyone who has recommended that you go ahead and support her in her desire to read.
Here are some things that will help that I think have not yet been mentioned:
1. Phonemic Awareness. It is very important for a child to understand that sentences can be broken down into parts (ie. words), and words can be broken down into parts (ie. syllables), and words can further be broken down into sounds and letters. Rhyming is one way to learn this (pat, cat, jat, mat, lat, etc. -- nonsense words are just fine) because you take off the first part and change it to another sound. Alliteration (like in alphabet books) is another way. Read lots of poems and rhyming books, sing songs, and do lots of word play. (Wordsaroni is a good book for that, if it is still in print.) Research shows that children who have good phonemic awareness in preschool or kindergarten are much stronger readers by 3rd grade than children with poor phonemic skills.
2. Direct instruction. The book Teach Your Child to Read in 100 Easy Lessons is a good way to teach reading, but it is pretty dry. You, the adult, follow an exact script and tell the child exactly what to do. If your child doesn't like this approach, just drop it. If she does like it, then go ahead, and balance it with a whole language approach.
3. Whole Language. This term has been somewhat discredited, but to me it refers to enjoying wonderful books, falling in love with books and reading, and using context cues to figure out what a word or sentence says. There used to be a big battle between the Direct Instruction folks and the Whole Language folks, but now we understand that children need both. If you use direct instruction, do balance it with reading books for the sheer joy of it.
4. Easy Readers. There are two series that I recommend. The BOB books by Scholastic are indispensable. They start with incredibly easy words that your child can sound out, and very slowly get more difficult. This is the only series that I have found that a real beginner can read. I also recommend the Brand New Readers series -- these are books that teach your child to pay attention to pattern, pictures, and context cues. (In other words, one series is phonics/direct instruction, the other is whole language.)
5. Great Children's Literature. You probably already do this, but I find that the quality of the books you read to your child is really important. Don't waste your time on boring books, or commercial books (like the ones based on movies or tv shows), or didactic books (the ones that try to teach a lesson) -- you will be bored, and so will she. Find the great books -- there are tons out there. I recommend Owl Babies by Martin Waddell, all of the Elephant & Piggie books by Mo Willems, all of the Pigeon books by Mo Willems, Brown Bear Brown Bear and other classic books with a repeating pattern, Where the Wild Things Are, Blueberries for Sal, the Olivia books, Stellaluna, all of Kevin Henkes' mouse books, No, David! by David Shannon, Hug by Jez Alborough, Swimmy by Leo Lionni, I Went Walking by Sue Williams, The Snowy Day by Ezra Jack Keats, the Napping House by Don and Audrey Wood, Traction Man by Mini Grey, the Scaredy Squirrel books by Melanie Watt, and all of the bug books by Eric Carle.
Happy Reading!!