Is there a word for "the length of time from birth to the age of majority"?
The word should be usable in place of any word that indicates a span of time, such as "week", "decade", or "saeculum"; specifically in the phrase "...once per [time-period]...".
The technical term (in legal use) is
minority n.
3. Law The state or period of being younger than the age for legal adulthood ....
[minority. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved November 18 2015 from http://www.thefreedictionary.com/minority.]
In non-technical uses,
child·hood n.
1. The time or state of being a child.
[childhood. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved November 18 2015 from http://www.thefreedictionary.com/childhood.]
serves the same function.
Minority. It applies to both the state and the time period:
the period during which a person is below legal age. (Collins English Dictionary)
the state or period of being under full legal age. (Random House)
Be underage:
- (Law) below the required or standard age, esp below the legal age for voting or drinking
The Free Dictionary
Nonage:
- (law) the state of being under any of various ages at which a person may legally enter into certain transactions, such as the making of binding contracts, marrying, etc
Collins Dictionary
Maybe "coming-of-age"? Not precise perhaps, and more of a phrase, but I think it at least indicates the period that lasts until one reaches adulthood...