It means he's a little bit stupid. Here's why:
1. Yes, a prawn is a type of small shellfish, and a cocktail is a drink or dish made by mixing several ingredients ( for example, you can have a fruit cocktail, which is like a fruit salad).
2. A prawn cocktail is a classic dish eaten as a starter to a meal. It's usually made of prawns or shrimps, with lettuce and Marie Rose sauce (pink and gloopy). It was very popular around the 1970s.
3. Now for the meaning. 'A prawn short of a cocktail' is part of an endlessly inventive set of idioms used to suggest that someone is not very intelligent: it basically means that they don't have a full set of functioning brain cells. Other common idioms are 'a sandwich short of a picnic' or 'a spanner short of a toolbox' - again, meaning that something is not complete. This style of idiom works like an internet meme: there is a basic formula suggesting that something is missing, and people can make them up as they go along. I've never heard anyone say 'a prawn short of a cocktail', but I know what it means because I'm familiar with the convention.