Let me clarify, it has not actually been confirmed that the whale is a dream. It has been said by a Nintendo representative however that the game starts with Link having a dream and waking up in Skyloft. Exactly like OoT started, with Link having a dream and waking up in Kokiri Forest.
The part about the whale being in the dream is just a theory, albeit a very plausible one. I think the dream encompasses not only the part with the whale, but the scenes with Link falling in darkness and seeing Phi as well. Link has had prophetic dreams before, so why not again?
First of all, Zelda is wearing different clothes from when Link and her go flying and get sucked in the tornado. No matter how you twist it, it's impossible that it's the same event.
Second, the scene with the whale seems very dream-like, with all-white background and a very dream-like effect, no to mention the slo-mo, with Zelda reaching out to Link as she falls. Granted, the slo-mo isn't a great argument, but still.
Third, the scene afterwards with Link falling suddenly has a completely black background. This is very dream-like, as the scene changes with the events and how Link, the dreamer, feels.
Last, I feel the whale looks more like some sort of metaphore for the 'evil' down below, than an actual creature, but this is more my opinion.
