I just found the 301A two tone with cabinet on Craig's list and bought it...In mint condition working with assessories...That's what your Singer is. Mine is from 1953 you should find the serial no. under the flip plate by the bobbin case. Mine also came with booklet so if you need any info re: care, oil instructions etc...just PM me.
And the feet dogs drop on it for free motion...screw by the bobbin case...
The closer I look that might be the 400 series..google singer sewing machines and you'll see pictures of all makes an models