Its seems reasonable to double it, treating it as if it's a die that always rolls the same result. After all, it's hardly a critical hit if it doesn't do anything.
The alternative, taking the "Critical Hits" passage literally, would not just impact unarmed strikes and creatures that do a flat 1 hp of damage. It would also mean that a DM choosing to take the listed average for a monster's attack would not double the result either, because there are no dice to roll twice.
There is plenty of room for someone to declare that by RAW, 1 hp damage attacks and taking-the-average monster attacks cannot benefit from critical hits. Though it's a fair literal interpretation, it's one that gives weird side-effects contrary to expectations of how both game and world should work. It's also RAW to use one's judgement where the rules seem to miss a corner case, and I think this is a clear case of one such corner.