I'm struggling with the title question in some of my current writing, so should you? Or is it just bad to repeat words? Other examples: "the remains remained", "she peeled the peel", "I am going to roof that new roof". It just seems like there are better alternatives.
Undoubtedly, no structures are banned, so to speak, from the English lanuage. It is all a matter of convenience and desired outcome. Sure, as a general rule, to quote @Zan700 from the comments, one tends to avoid repeating words with similar roots within a paragraph, let alone one sentence. This is to avoid sounding monotonous, of course, and unintelligible - said the English teacher. Hence your sentence could be paraphrased as, "He had a laugh" or "He laughed at that;" both convenient - oops, say "suitable" - choices which I am sure you would have no trouble coming up with. However, it is perfectly alright to repeat the roots as often as we want, with the clear and consistently emphasized intent of a dramatic effect. You should make sure that if you use them as a narrator, you reference the instances as much as possible by repeating the unconventional structure where possible. If you use them as a character, (creepy circus clown, I suppose?) you should repeat the structure enough times to make it clear that it's a trait of the character and not lack of vocabulary or interest in your writing from your end. Finally watch out for potential pitfalls in using words that are very similar as they might disturb the reader's flow. As an example, consider, "They laugh a laugh all the time." This will make the average reader pause and really consider the structure at least momentarily. Hope that helps!