Side A matrix 3537
recorded Nov 2, 1948, Hollywood, CA
Side B matrix 2718
recorded Dec 1, 1947, Radio Recorders, 7000 Santa Monica Blvd., Hollywood, CA
with Dave Cavanaugh's Music
Featuring Red Norvo, vibes; Arnold Ross, piano; Jack Marshall, guitar
... and "So Tired" was actually the A-side. Capitol, like some other labels, had a coded side designation in which the "y" under the matrix number meant the top side and the "z" meant the flip side. See the comments on Capitol 1010, among others.
I have flipped sides on this record accordingly (see also SearchWorks). I have also added the exact recording date and studio for the "z" side (from praguefrank's Kay Starr sessionography/discography).
Your release date guess (December 1948) is somehow confirmed by the Billboard mentions, first in a Capitol advert in the December 4 issue (page 29). As "So Tired" already made the Most-Played Juke Box Records chart in the following Billboard issue (for "Week Ending December 3"), a late November 1948 is distinctly more probable though. I've corrected it like that.
This is one where the early matrix number doesn't make sense for the A/B side allocation.
So Tired was a hit in January 1949, and was a hit in Nov 48 for the composer , Russ Morgan. Steady Daddy was recorded a year before going by nearby matrix numbers (Benny Goodman and Peggy Lee recorded matrices 2722-2728 on 12/2/47) so it looks like Capitol used an old recording to back the 'rushed out to compete over christmas' recording.