“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.
Feel free to teach your child whatever you’d like, language is totally fungible.
The reason I’d suggest not to is because speaking in this way will, in fact, cause people to think less highly of you.
It’s not a matter of principle and “formal correctness” is pretty meaningless in human language, but “don’t speak in a way that a substantial number of people regard as incorrect” is a meaningful goal!
I would argue that people who think less of a three or five years old because the kid said "I did an ouchie" are simultaneously irrelevant and frankly dumb themselves. Kids life wont be affected at all.
Your claim is really based on fairly absurd notion that a sentence normally used in relation to the kids will somehow set the kid apart from their peers ... who listen to the exact same sentences. As in, the problem of kids speech somehow damaging kids long term is literally non existent in real world.
Miniscule percentage of parents takes offense on it and nobody else cares.
Obviously we’re talking about kids acquiring language, I.e. should the response be to nudge them toward more accepted language as they develop, or make up silly overintellectualized arguments like “hmm, well I can understand what they mean! [insightful face emoji]”
“Aww cute!” responses to incorrect language is how kids develop speech impediments.
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.)