[The Squatter of Amon Rûdh]

I would say that the whole concept of an official, rigidly-enforced minimum age for smoking (or drinking, for that matter) would be antithetical to the whole conception of the Shire, which inclines towards a mild combination of feudalism and anarchy. According to the Prologue to The Fellowship of the Ring:

The Shire at this time had hardly any 'government'. Families for the most part managed their own affairs.

This being so, and bearing in mind the description of the Mayor of Michel Delving's duties, I should say that it was up to the leaders of one's extended family to decide when to permit either, but we must bear in mind that the Shire doesn't have any moral objections to either smoking or drinking, so that the decision would be based on a feeling on the part of older Hobbits that a particular youngster was ready to be introduced to the art of pipe-smoking or the delights of the brewer's art, rather than on any hard-and-fast rule. In any case it would seem more in-keeping with Hobbits' general outlook that such matters be decided on the merits of each individual case rather than on some official edict. I expect that they would view our modern governments as interfering busybodies and who am I to argue?