The pedal is an "Epic" Which would date from 1934-54 if its original to the set.
The snare, depending on the strainer might be a Student Model Radio King.
If it has:
A 3ply shell
No RK Snare brackets
No engraved hoops
Or if it has a solid shell it would be a Gene Krupa Radio King.
Also the set looks to be a Swing-Master Ensamble. (Probably) A 12x22
bass drum and a 8x12 or 9x13 tom (in the catalogue it lacks a tom size listing.)
But I think this is a Swing-Master set because the bass drum has double
tensioned lugs while the tom has single tension lugs. Also these were only
available in a duco or lacquer and they came with one cymbal holder like yours and it came with a wood block and cowbell.
Beaut of a set you've got there. If the heads are calfskin this is probably a
fifties set but the age could befrom 1948-55. Pictures of the interiors, snare
strainer would help.