Do nits have brains?

The head louse is an insect, and insects have a somewhat more complicated arrangement than vertebrates when it comes to neurological features such as a 'brain'. Your central nervous system comprises the dorsal nerve running through your spine, and your brain and its associated structures in the cranium. An insect, however, has a number of ganglia located along a central nerve chord for each segment of its body- the two in its head might be considered its actual 'brain', but one should note that as most insects can survive, and variously maintain relatively normal behaviour, feed, mate, and even retain long-term memory after decapitation, it's not all located in their heads.

So, yes... nits have a 'brain' that governs their behaviour, activities, and responses to stimuli, but unlike with zombies, head shots are not your best defence.