Well, that version never got made, but these records did, in 1944, featuring Rogers and the songs and other music that apparently had been written for the film by children's music specialist Frank Luther and composer Victor Young.
This information comes from an excellent Alice in Wonderland site, which shows the much more colorful artwork that was on the original 78 rpm album - artwork thatwas done by Disney. What you see here is the 10-inch LP reissue from 1949.
To portray Alice, Rogers seems to be doing a sort-of Shirley Temple imitation and speaking as rapidly as possible. An unusual approach. But what's more unusual is the voice of the White Rabbit - it is, with perhaps deliberate irony, Arthur Q. Bryan doing his Elmer Fudd voice. Children must have found this very confusing!
