Need Help Remembering a Game Title

This, is a rather old game, and had to be out by at least the year 1996, and that's probably even stretching it by a year or two . It was on floppy discs, man. It's old. And yeah, this should be fairly obviously, but it's a PC game.
 
You're an adult and you go to this carnival. You play some stupid water gun game with the moving targets, and when you win, you get to choose from three different dolls (depending on which doll you pick, that's the difficulty the game is set at). Once you touch the doll, you get sucked in, becoming the doll and landing on this remote, tropical island with very few inhabitants who give you puzzles to solve in order to get their items and get off the island. So it's an indepth puzzle game/point and click adventure.
 
I remember having such a hard time with this as a kid, especially since I found the dolls to be rather creepy. I need to know what this is called. 
 
EDIT: Just remembered a few more details. You're gathering these items as ingredients needed to be taken to this huuuuuuuuuuuuuuge pot to make this concotion to get yourself back to your normal self. The doll makes a funny face when it drinks the stuff, and the music is creepy.

That sounds weirdly familiar.  Is it a coincidence that I don't remember what Day of the Tentacle was actually about?

Ooooooh. I feel like I should know this...ugh...what is it called again?

Floppy disks?  Couldn't tell ya.  I don't remember much of those anymore.

Amen to that.