It is just a different sound for the same thing. There is nothing dumber about "I did an ouchie" then "I got hurt". Ouchie is more infantile, but not stupider.
"I did [a noun]" is 'stupider', i.e. not grammatically correct English, i.e. a formulation that people will look down on you for using as you age. Sometimes you have to teach children things they'll eventually have to unlearn, but this is not one of those occasions.
“I did [a noun]” is grammatically correct English object-verb-direct-object sentence structure.
Depending on the noun, it may not the most idiomatic way of expressing the sentiment it intends to communicate, but that is a different issue. (On the other hand, idiom is context dependent, and the objection here seems to be that it is idiomatic in at least one context, but that people prefer that children exclusively learn some other preferred idiom. But if you don't have this diversity, children don't get to learn and practice context switching as early, and that's an important skill, too.)
"I did a runner" British idiom means I ran away without paying. The only problem with "I did a water" is I don't know what "a water" is without context. If person A said "I did a shot" and person B said "I did a water", it would make perfect sense.