Children want to learn to read at very different ages. I think it can be a huge boost to their confidence if they enter school already reading, but only if it is just one of many things they happen to like doing.
My son learned to read very early, partly because we were travelling a lot, and looking at books or fooling around with writing was a good thing to do on airplanes and trains to keep him entertained and happy. He happened to be very interested in letters and numbers, as some children are.
It sounds like your daughter is also interested, and you are not too pushy, so why don't you see it as something fun to do together, with no particular feeling that it is more or less important or significant than any of the other things she likes doing. If you follow her lead, you shouldn't go wrong.
I think magnetic fridge letters and scrabble letters, and putting up post it notes with one word on them can all be fun. You can read street signs, the letters on car registration plates, find the letters of her name, etc. I think it is fun for them to recognise various letters as they walk around, rather than teaching them words.