During more crowded times (like mid-afternoon), it might be a good time to check out various shows around the parks. We saw Mickey and the Magical Map in Fantasyland, the Tangled Show in Fantasy Faire (would have loved to see the Beauty and the Beast show too, but didn't have time), the Disney Junior show and Frozen shows in California Adventure (though Frozen will probably be very crowded also). They were all great! Our DD is 4 as well, and she was a bit restless about 1/2 way through, but it was a long show. The other shows aren't nearly as long, and she did great with them.
Characters might also be a good thing mid-day also...especially the ones that randomly appear in various places (rather than having actual queues). Lines can't form really until the character appears. I'm thinking of Peter Pan and Captain Hook (they appeared together by the Pixie Hollow exit when we were there), Aurora I believe meets at the wishing well? I think another princess meets there too, alternating w/Aurora. I don't know how your DD is with people in costume, but the first time DD went to DLR last year she was afraid of the fur characters, but totally fine with the face characters. THis year, at 4, she was pretty good with both face and fur characters. Just be prepared for characters maybe not going over so well.
There's always Musical Chairs w/Alice and the Mad Hatter at Coke Corner (ask a CM at Coke Corner in the morning what time Musical Chairs is at).
DD's absolute favorite ride is the teacups. It's never been a favorite of mine, but the first time she rode it the pure joy on her face was infectious. It's now a must do every trip. So I would definitely suggest doing rides you might not personally be a fan of...your child might be!
Also, the best advice we had with introducing DD to Disneyland last year was to try and terrace her ride experiences. We started with outdoor rides like Dumbo/Casey Junior/Storybook Canal Boats/Jungle Cruise, etc....then moved on to not so scary dark rides (Peter Pan, Pirates, Alice in Wonderland, it's a small world, etc)...then the "scarier" dark rides..(Snow White's Scary Adventures, Mr. Toad's Wild Ride, Haunted Mansion Holiday, etc (DD totally giggled in the stretch room that year
). This year she was finally 40", so we added in Gadget's Go Coaster, Soarin', Big Thunder Mountain and Star Tours (she did NOT like the Naboo scene in Star Tours at all, but was fine with all the others we saw..we rode it 2x). I do think introducing the attractions that way really helped DD not be scared by the time we got to the scarier dark rides.
I hope that helps a little! This thread is great for questions..everyone here is very nice and helpful.
Feel free to ask whatever you need!