しよう is the volitional form (short form of しましょう), but どうしよう is more like "what should I/we do." In this case, he's just wondering what to do.
どうするかな sounds like he already knows what he's going to do, but he's not going to tell the other person (like he's teasing or something). Or it means that he's talking about someone else (ie, 小林 [kobayashi] is referring to a third person, and he doesn't know what their plans are for the summer vacation). Due to the lack of pronouns, the use of どうしよう is the indication that B is referring to himself.