Hi C.,
Yes, hiccups are very normal. My son had them very often when he was younger (he just turned 2 last month) and it would drive me batty b/c it would keep him from being able to sleep sometimes.
With the permission of our pediatrician, we would give him a dropperful of Gripe Water, which is a natural anti-hiccup/gas/colic liquid found at Babies 'R' Us, among other places.
It worked AMAZINGLY well! By the time he was done taking the liquid from the dropper, the hiccups were GONE---almost INSTANTLY!!! The key was to have him take the dropperful very slowly, making multiple swallows (or go ahead and add a dropperful...the actual dosage for a 20-month old is more than a single dropperful, but the hiccups go away so instantly, you may be able to conserve, like we did).
If it happens to be a meal or snack time, then give her her sippy cup or bottle instead of using the Gripe Water. We found that if our son gulped down a liquid---again, multiple swallows---that would make them go away, too. I guess it disrupts the rhythm of the hiccups?!
Anyway, there are a couple of things to try! I hope they work for you...and GOOD LUCK!!
D.