I have known 2 Dorits, both British and their parents were from Israel, both pronounced their names just like "door•it". Emphasis on "door" with at quick "it" on the end.It makes me think of the Charles Dickens character and story "Little Dorrit" also pronounced "door•it".
Miss Claire is usually correct on these matters. The first syllable of the Hebrew boy's name Doron (I knew an Israeli called Doron) is pronounced Doh and at first glance there's no obvious reason why the first syllable of Dorit should be different. It would be great if someone from Israel would tell us the undisputed way!
It makes me think of the Charles Dickens character and story "Little Dorrit" also pronounced "door•it".