It could be that horcruxes performed on things with brains are intensely unreliable -- so, instead of the brain being able to assert itself over any dumb matter it's bound to, like a book, it suddenly finds itself fighting for control with matter that has a 'soul' of its own. In this case, the horcrux gets trapped in the brain of an infant child, and you sort of split the difference - the horcrux is partially destroyed by years of being trapped in a baby brain, but leaves certain skills and intellect and preferences behind, integrated into Harry's brain.

An alternative hypothesis is that the horcrux is inactive, or unconscious, in some form, and has been integrated into Harry's brain, and Quirrelmort has a plan that involves waking it up at some point in the future if Harry can't be pushed into his dark side by subtler means.