SmartChoiceMusic.com is offering an album by Stuart Hamblin called "Prettiest Girl in Town, Vol. 2" which contains BE JUST LIKE YOUR DADDY. Unfortunately, it's a British company, and perhaps their albums are available only in the UK.

The University of North Texas library has a copy of the sheet music of PLEASE BE LIKE YOUR DADDY, from 1942.

The Southern Folklife Collection at the University of North Carolina at Chapel Hill has a copy of a songbook called "Stuart Hamblen and His Lucky Stars, Deluxe Edition" (M.M. Cole Publishing Co. Chicago, Ill. 1942) which contains PLEASE BE LIKE YOUR DADDY.

WorldCat might help you find a copy at another library.

Some libraries will copy something for you and mail it to you, for a fee.