May a linking verb be omitted in a sentence with compound subject?

Consider the sentence:

Our son, John, is 15 and our daughter, Mary, 11.

Is it grammatical? I have read such omission of the linking verb (especially is) in a sentence with a compound subject. I wanted to know if the linking verb attaches to both the subjects. Is the above preferred to the more straightforward (and grammatical) construction:

Our son, John, is 15 and our daughter, Mary, is 11.

?

Our son, John, is 15 and our daughter, Mary, __ 11.

Yes: it's grammatical.

This is called 'gapped coordination' (or 'gapping'), which occurs when the middle part of a non-initial coordinate is omitted but recoverable from the corresponding part of the first coordinate.

The gap marked __ is understood by reference to the first coordinate, in this case "is".

I prefer the version without gapping, especially in speech, but usage varies.

Edit: Here's a link to Wiki's article on gapping link