I wouldn't use a .410 slug on a deer anytime.
I think the idea of a 243, or, even better, a 260 Rem in a full sized rifle with a "youth" sized stock would be a MUCH better choice. If you have to go with a shotgun, then a 20ga would be the minimum I would recommend.

"Progress, far from consisting in change, depends on retentiveness..those who cannot remember the past are condemned to repeat it." Santayana