Mac - eventually, as your projects grow, so will your list of tools.
now may be the time to visit some pawn shops in your area to
look for a 1/2" VSR electric drill with low RPMs that give high torque.
well worth the investment - especially in this project.
with a hefty electric drill and a sharp Forstner bit, I bet your hand/eye
coordination improves tremendously drilling all those holes freehand.
(and IF you did make a jig, you would probably be ditching it after half a dozen
holes - and going freehand for speed vs accuracy.
it's a Jungle Gym for kids - not a piece of living room furniture - don't overthink it.
looking forward to seeing your project filled with yelling and squealing kids !!
(that could care less if the holes and dowels were perfectly aligned - or not).
looking closely at your initial design, I would suggest you go over/under the
dowels vs going through them at the intersections.
this is my "Go To" drill for anything that needs some extra UUuumphh that
a battery drill can not provide. the side handle is CRUCIAL to safe operation.