I emailed Mojang's Support in order to get some official words on the subject. Here is Marc Watson's response:
There's bits of truth in various comments in the thread you've linked. The intent here is that we don't want people buying an account and then sharing it between friends, who should all have their own account. We've even seen things like sharing sites, where they basically rent out accounts, and that's definitely against the rules.
I don't believe that we're interested in looking too deeply into whether a parent or a child is logged into a particular account at any given time. This would be difficult (or impossible in some cases) to determine from a technical standpoint anyway. I would say that as long as the use is fair and reasonable, a parent or child doesn't have anything to worry about.
(Emphasis mine). As mentioned in the email, Mojang considers parent/child use 'fair and reasonable' use of a license. However, sharing an account between friends or online would not.
Which is in accordance with what I originally deduced here:
As per the EULA you linked (emphasis mine):
The one major rule is that you must not distribute anything we've made. By "distribute anything we've made" what we mean is "give copies of the game away, make commercial use of, try to make money from, or let other people get access to our game and its parts in a way that is unfair or unreasonable".
You aren't doing anything they've listed above. For example, You aren't:
- Giving copies away
- You are still only using the one copy of the game
- Making commercial use of it
- An example of this would be owning a cafe, and having your copy of Minecraft available for patrons to play in the cafe.
- Making money from it
- Directly loaning or selling your account for money
It would be 'unfair or unreasonable' for you to both log on at the same time however - You say this isn't going to be the case, but in future, if you decide to do this I suggest you purchase your child their own account.