A 19 month old child can simply not see it from any perspective other than her own. Making her apologise will make you feel better and thats about it. She doesn't understand cause and effect. You need to observe her to determine why she is lashing out. Rather try to redirect her behaviour to something more positive. Most importantly, praise her for good behaviour.
She is using her body to react because she doesn't have the speech needed to say what is making her unhappy. Only child, no I doubt it is the problem. Children of that age lash out in various ways, from tantrums to biting to hitting. You need to determine the cause.