The version in the DT doesn't list the source. For what it's worth, my copy of Ludlow Music, Inc's "Woody Guthrie Folk Songs" has the following words:

DO RE MI
(Woody Guthrie)

Well, thousands of folks back east, they say, are leaving home most ev'ry day
And they're beating the hot old dusty way to the California line
Cross the desert sands they roll a-getting out of that old dust bowl
And they think they're going to a sugar bowl
Here's what they find
The police at the port of entrance say
"You're number fourteen thousand for today."

Chorus:
If you ain't got the Do Re Mi, boys
If you ain't got the Do Re Mi
Well, you better go back to beautiful Texas
Oklahoma, Georgia, Kansas, Tennessee
California is a garden of Eden
It's a paradise to live in or see
But believe it or not
You won't find it so hot if you ain't got the Do Re Mi

Well, if you want to buy you a home or farm
That can't do nobody harm
Or take your vacations by the mountains or the sea
Don't swap your old cow for a car
You'd better stay right where you are
Well you'd better take this little tip from me
'Cause I look through the want ads every day
And the headlines on the papers always say, oh . . .

Joan