Liam, it appears that the first draught problem was probably in the Torquemada book in 1547, generally considered the first checkers book, as mentioned in the ACF Origin of Checkers page.
This book is mysterious, but it appears to have problems in it as a mid-sixteenth century book published in Valencia, Spain is referenced to have at least one problem. The reference is from a 1591 book on draughts by Pedro Ruiz Montero. Dr. Govert Westerveld's site has an essay on the 1635 Timoneda book. That book is in Spanish, but published in Toulouse, France. Adding to the mystery is Timoneda died in 1583! Dr Arie van der Stoep's site has a draught problem from a 1595 Spanish draughts book by Alonso Guerra. The problem is in the Evolution of the Game
page, Step 5. The problem you presented may or may not be the first draught problem; it is just the first draught problem predates 1635 by decades....The two draught historians cited may be conveniently visited from the FMJD history page. http://www.fmjd.org/?p=genhist