DD is the same age (3.5) and loves anything that involves actively playing with letters/phonemes (me writing things for her, trying to write herself, writing on the computer, playing with magnetic letters).
We live abroad and so I'm teaching her to read in English, on a slow and gradual basis. She's always been interested in letters and sounds, although like anything else it tends to go in phases. She's at the same stage as your DD in that she can hear the sounds in CVC words and, going the other way, can blend them together. So I bought her the first Songbirds set to see if she was interested, but although she was enthusiastic about "some books I can read by myself", something didn't click - maybe because they don't seem like books as she knows them (the Usborne ones are different on that count, obviously). She's more interested in picking out occasional words from her actual books - she finds it especially funny when they're elongated words such as "Aaaaahhhhh" and "Sssshhhh" and Muuummm" from Charlie and Lola.
So I stick to the writing and drawing-based things that she enjoys. Basically, if it involves felt tips and a pad of paper, she likes it. Something she enjoys a lot is when I make up those "join the word and the picture with a line" games, the sort you find in activity books - five or so three-letter words, then draw five pictures next to them in the wrong order, and she works out what the words say and draws a line to the right picture.
(Last time she said "It's my turn to do one for you!" So she wrote "ioa" - about the only three letters she can write. Then she said "What did I write? - Eeeyore! and did a picture of Eeyore.)
We seem to do a fair bit over breakfast on weekend mornings, as it comes up - e.g. today she started wondering what made ball and suggesting "b, then u", so I wrote down all the words ending in -all I could think of.
She goes to a Montessori preschool (in Czech) where the philosophy is - if they're interested, go with it. They do Czech literacy things with the older children and they have no objection to the younger children joining in - they wouldn't if they weren't interested, is their way of looking at it. (Also, Montessori herself said that children are interested in "writing" before reading, and I think there's a lot in that).