I'd vote for crediting both _Margaret_ O'Brien and Billy May.
A Google search shows that the record album Capitol CC-71 was copyrighted on March 22, 1948 per the Catalog of Copyright Entries and is announced in Billboard, Mar. 20, 1948, p. 115. I've updated the entry above accordingly.
I have filled in the year of release based on information submitted with surrounding numbers. The most probable month of release is February or March. I would be less than honest, however, if I did not mention that there is at least a small possibility that the disc was issued as early as December, 1947, or as late as March, 1948.
It would seem to me that "Original Story by Marissa O'Brien" should qualify that lady for a composer credit on both sides. There is some ambiguity in the phrase "Music by Billy May". He was probably the leader of the accompanying orchestra (well known for that at the Capitol studios) but might also have composed the musical score (he was a truly famous arranger as well). Whether he should get a composer credit or not is probably an editorial/executive decision.