You’ve got me pegged” here means “you have me figured out.” Example: I think you’re more interested in music than books. You’ve got me pegged. Means it’s true than you are more interested in music.

you got me pegged - you have assessed me correctly from the New Oxford American Dictionary on my computer verb (pegs, pegging, pegged) 1 [with object and adverbial] fix or make fast with a peg or pegs: drape individual plants with nets, pegging down the edges. 2 [with object] fix (a price, rate, or amount) at a particular level. • informal, chiefly North American form a fixed opinion of; categorize: the officer probably has us pegged as anarchists.