In the scene with the DNA analyzer, she shows K what looks like the wooden horse but K will not fetch the horse until he goes to the scrapyard and finds it in the furnace. Is she able to somehow access K's memories? Or has he described it well enough for her to make this virtual copy?
I am rewatching the flick right now and somehow Joi shows K an apparently exact duplicate of the horse before K gets the physical object from the furnace at the scrapyard -- very puzzling.