I'm an infant & toddler physical therapist and I see a lot of babies with reflux who hate their tummies. They already have a lot of pressure inside then lying down on the tummy makes it hurt more.
Tummy time is very important for developing neck muscles but also for strengthening her arms & shoulders. The challenge is finding ways to get her to put weight on her arms, learn to lift her head and keep some of the pressure off her tummy.
This brochure gives lots of ideas on how to sneak in tummy time throughout the day: http://www.apta.org/AM/Template.cfm?...ontentID=50825
If she is not able to lift her head yet, I would help her by getting her arms in a good position. Look at the picture of rheanna's beautiful little girl with the green bib. See how her arms are in front of her body? Try this but bring her elbows a little closer so that they are in line with her shoulders. Help her by gently lifting her shoulders for her. This makes it a little easier to lift her head because she doesn't have to lift her chest also, but it also allows her to keep weight on her arms.
Kneeling over a boppy, sofa cushion or over your leg also gets the pressure off her tummy but allows her to put weight on her arms while taking away some gravity. Again, get her arms in that ideal position (elbows in front, propped on forearms).
Short intervals several times a day is best when you're just starting. Once she is able to lift her head and reach for toys, she should enjoy playing on her tummy.
ETA: If she is still not picking up her head at 4 months, I would contact your local early intervention program. I tried my best to explain in writing, but they would be able to give you more specific positioning ideas in person. If you are concerned about anything with her development, it never hurts to get an evaluation. Feel free to PM me with any questions.