Going by the development of the Hebrew language you are probably right. Sara may be older than Sarah. No vowels were written out in ancient Hebrew (and aren't in modern except children's books and difficult words). But at one point the massorets (the scholars who passed on and watched over the biblical scriptures) were afraid the meaning might get lost on the way and so they added consonants at certain places indicating in fact vowels. A J would mark an I, an Aleph would stand for an A (the Greeks made it an A later), and also an H would be added, where an A was not written out. Like in Sarah.
Later the massorets invented a system of little dots and lines to indicate the actual vowels. But usually the additional consonants were kept. (They had a funny name: "mater lectionis" = "mother of reading".) This applies to vocabulary words, with names I'm not sure. (It has nothing to do with the alphabet though.)
Now in the case of Sara/Sarah I don't know. In the bible you will only find Sarah, but in the Greek version of the Hebrew bible there is Sarra with a doubled R (for whatever reason), and the Latin Vulgata kept it that way.