I do believe that your sentence above is grammatically correct, however using it will make writing sound more informal. Even using the contracted form of 'have' with a singular word such as 'child' will immediately make the words sound less formal. For example:

The child's eaten.

As opposed to the more formal:

The child has eaten.

This might be due in part to the fact that usage of contractions must have developed after people began to use common word patterns in everyday speech. Generally, in my experience, people will speak in a more informal manner than they write.

To a lesser extent, if you wish the writing to preserve a degree of formality but are looking for a way to put a contraction in then it might be slightly better to use a preposition in place of the noun:

They've gone for a walk.

The same rules apply for plural nouns. If you wish for the style of writing to be formal (e.g. a job application letter) then it is better to avoid contractions as a rule of thumb.

I do believe that your sentence above is grammatically correct, however using it will make writing sound more informal. Even using the contracted form of 'have' with a singular word such as 'child' will immediately make the words sound less formal. For example:

The child's eaten.

As opposed to the more formal:

The child has eaten.

This might be due in part to the fact that usage of contractions must have developed after people began to use common word patterns in everyday speech. Generally, in my experience, people will speak in a more informal manner than they write.

To a lesser extent, if you wish the writing to preserve a degree of formality but are looking for a way to put a contraction in then it might be slightly better to use a pronoun in place of the noun:

They've gone for a walk.

The same rules apply for plural nouns. If you wish for the style of writing to be formal (e.g. a job application letter) then it is better to avoid contractions as a rule of thumb.