Since she is only 19 months old, she doesn't have the verbal skills yet to express frustration, anger, or sadness, so hitting at this age is definitely a "normal" behavior. Your job now is to teach her how to "appropriately" express her feelings, and help her figure out how to "get over it" (not really the phrase I want to use...just can't think of the *right way to say it*).
When my son acts inappropriately, his dad and I tell him, "This is not the way to tell us what is wrong, Honey." Then we play "20 questions" to try to figure out why he is mad, and help him learn how to express his feelings in a better way. (Yes, this is the age where you get to play "detective" on 364 out of 365 days!) This is going to be a very frustrating year for you (and her), but as her verbal skills increase, the hitting should stop.
My son is about to turn 3, but is very speech delayed, so you can imagine the frustration levels at our home right now! Hopefully, we'll be able to get him into Preschool this fall, and his speech will "catch up" to the rest of him!
Good Luck with this issue, and Hang in There!
~J.~