Assuming it takes someone roughly 4-6 weeks to realize they are pregnant, the child was probably born in or around November 2014, and will be turning 10 in the next couple weeks.

I suppose the woman filming the video could have taken much longer to realize (unlikely, but possible), or chose to wait to tell the father until several months later (also unlikely, but possible), but either way, the kid is turning 10 now-ish, not 11.

It's also possible that this video was posted well after it was taken, in which case we can't say much about the age of the kid, except that it likely happened before this "Share to YouTube" functionality was removed from iOS.

Presumably there are still about 9 months to go in that pregnancy before the child is born.

I always thought, that would make way more sense. But a bit harder to find exact dates probably ..

Only if your culture measures age from conception instead of birth.