You totally need to get the book Healthy Sleep Habits, Happy Child by Dr. Marc Weissbluth and read it cover-to-cover! It will be such a great help for you and her.
It sounds like you are doing a lot of things right: go to bed awake and fall asleep on her own, 12 hours at night, making good use of the awake time - right on and kudos!
A few things to keep in mind - at 4 months, she is probably RIGHT at the beginning of developing a good, strong morning nap. Work on that one first. After she wakes up in the morning, start soothing her down after about 2 hours of playing. Look for signs of drowsiness and follow her lead if she can't make it 2 hours (don't force her to be up 2 hours if she's ready to sleep; this will lead to overtiredness, fighting taking the nap, and possibly a shortened nap). Use a consistent pre-nap soothing routine (since she's great at self-soothing and going to bed drowsy but awake, this doesn't have to be long, just consistent). Finally, at about four months this morning nap starts to emerge so although she might not 'go the distance' just yet...keep in mind she's probably ALMOST ready to do so!
Feel free to PM me with questions you might have. We had fantastic success with our first child (although we started the nap schedule at 6 months and not 4 months). Now that we have a 3-week old, we are totally in tune with our child's sleep cues and need to sleep and even though he is only 3 weeks old, his sleep patterns while not yet solidified are exceptionally predictable and he follows a great, self-directed routine because we're very vigilant about watching for cues and respecting his need for sleep.