Hi there-
Both of my kids had/ have reflux. I have a 4 1/2 year old who grew out of it around 2 years of age and an 8-month old who still suffers with it. Both children were born at 37 weeks and yes, prematurity plays a role. Their systems just aren't full developed yet.
You can expect that she will out grow it. My son took a little longer than usual. They usually outgrow it by one year of age. You can also expect that they will be more susceptible to colds and infections because the acid coming up into the esphogus causes irritation and because their nose/ throat is so close together there is more chance for infection. Watch your baby to see how symptoms develop. If they interfere with her eating and sleeping, it's time to call the doctor. Otherwise, just realize that it's par for the course.
My children never completely stopped refluxing even on the Zantac and colds always made it worse because of the refluxing. You should always take caution never to feed her unless she is in a reclined position and keep her upright as long as possible after feeding. Keep an eye on your child as she grows to make sure that her dose is appropriate. If she starts refluxing more, than it's time to increase the dose.
Also, she will do better once you start her on rice cereal because it is more solid in her system. Try not to give juice for awhile because of the acid and extra liquid. You may notice that she wants to eat smaller and more frequently. Reflux babies do this to comfort themselves.
Finally, both of my babies slept on their bellies. I know this is taboo and I was deathly afraid of SIDS but I was more afraid that she would reflux and choke on it if she was on her back. So, for the first 6 months, I slept in her room to help keep her safe.
Sorry that this is so scattered. I hope this helps and please feel free to e-mail if you have any other questions.
Ps. DO NOT put her on Reglan. This is a bad drug.