This is an example of a specific pattern of joke. It isn't a common idiom in English. The pattern is "He's X short of Y," and it always means unintelligent or slightly crazy. The game of the joke is to find fresh and surprising phrases for X and Y. One list of them can be found here, but there is no definitive list because the whole point is to surprise your friends by inventing (or, more likely, repeating) one they haven't heard before. http://dan.hersam.com/lists/not_bright.html

"I think you're a whole hamper short of a picnic" means that you (the speaker) thinks the other person is less intelligent. Or stupid. A 'hamper' is a basket used to carry food, and if there is not enough food, than we can't have a picnic. So the phrase means with no food, there is no picnic. With no brain, there is no intelligence.

The person who said this isn't too bright either, by look of it, or at least he/she doesn't have a very good grasp of grammar. As I'm sure you know, it should of course be: "You're a whole hamper short of a picnic" ( not 'your') This is an extension of the more common insult 'You're a few sandwiches short of a picnic' , which suggests that the person has a few brain cells missing. In this case, the speaker has taken the insult a few steps further. The picnic not only has a few sandwiches missing, but an entire hamper (or picnic basket). Or in other words, he/she has no brain at all.

What do you think a hamper is?

A similar variation is: "He's not the sharpest knife in the drawer" or "He's not the sharpest tool in the shed". When a person is described as being "sharp", it implies that they are clever, observant and quick-thinking. So, it's quite popular to play on words involving objects which are sharp, like knives and tools, to convey that someone is perhaps a bit slow or dim-witted compared to others.