Over on ismacs.net
Singer New Family Sewing Machine Information (ismacs.net) look at page 5, 6, or 7 of these ads, tough to tell on pages 6, 7 as the cabinet doors are closed, but you can read the descriptions. The picture on page 5 has 6 drawers, yours has 4.
Also over here
Singer Sewing Machine Letter A, Number 1, Turtle Back, New Family (singersewinginfo.co.uk) based on the date you have I'm going with a Singer New Family.