This is - unfortunately - completely incorrect.
I can't tell if the HoC will accept the amendment or not.
However, it is not unconstitutional. First of all, nowhere in the Constitution of Canada (= the several laws comprising the Constitution, British North America Act and so on) does it state that 18 is the age of majority and that you have to be 18 to apply to the government for anything.
Also, you misunderstood the amendment. Even if this amendment passes, a minor may sign the application but it must still be countersigned by a legal guardian. For example, a minor refugee child has a legal guardian assigned to them who would countersign the application. This legal guardian is not their parent! So far, without the amendment, no one could file an application on the child's behalf unless the actual parents (adoptive or natural) apply at the same time or are already citizens. Not even a legal guardian could do it. This is what the amendment changes. Note that even under the current law, when a child of Canadian parents applies for citizenship, it is the child who applies. It is the parents who sign for the child but it is still the child who applies. That is already the case.
Again, nothing about this amendment is contradictory to other laws or custom. And it is definitely not unconstitutional.
It is also generally incorrect that minors do not have any legal capacity. For example, a minor has all the legal capacity to agree to a trade within usual limits. For example, every time a child buys a pack of chewing gum, it goes into a legal contract with the seller. You seem to misunderstand the term "legal capacity".
And I can guarantee that this has nothing to do with sex, gambling or smoking pot. I promise
The HoC might not accept this amendment for many other reasons of course.