How to properly nurture a "gifted" toddler?

Today we found out that our 16 month old is "gifted" or very advanced cognativly/socially/imaginativly for her age. The pedi basically just said to read to her constantly, allow her to play with others often, and also do skill based games (puzzles/blocks/shapes) with her. Does anyone else have any experience with a "gifted/advanced" toddler? I dont want to turn her into one of those geeky freak kids who skips 5 grades, but I also don't want to hinder any abilites she may grow to have. I understand at this age it is more of a developmental quotent then an intelligance quotent, however there are other correlating facotrs that she exhabits to leave her pedi to believe she is/will continue to be "gifted". Any suggestions/advice?