When it comes to little kids, simple costumes are the best; they won't like being put into something complex, and you also shouldn't spend a lot of time and money making something that they won't be able to wear again and might mess up in the simple course of being a kid. So it's best to stick to things that can be implied with two or three simple pieces, like cartoon characters. For a little girl (up to about age four), you can make an adorable Cindy Lou Who costume (out of "How the Grinch Stole Christmas") with a pink nightie, some bows and pipe cleaners. You can find a great picture of the character here. (That's the cartoon Cindy Lou; if you want a costume from the Jim Carrey movie, there are plenty of places to check, but your little girl will have to be older-and there will be some serious hairdressing in your future.)
Cindy Lou's nightie is bubblegum pink, with long sleeves and a long skirt. The hem, neck and cuffs all have ruffles, also pink. Any long pink night dress will do nicely, though if you can find one with the ruffles it'll enhance the effect. If you're handy with a sewing machine, you could probably make one with little trouble and only a yard or two of fabric. Of course a real child can't be put into a dress with such a tight hem, but as long as the nightie is pink everyone will get the idea.
In her hair, Cindy Lou has two bows. They're either fuchsia or red, depending on what picture of the character you check; I'd say, pick whichever color looks right to you. You can make the bows with grosgrain or velvet ribbon, either tied or glued to a pair of barrettes to go in your child's hair.
Finally, the "antennae". Though they aren't near the bows in the pictures of Cindy Lou, for costume purposes it's probably easiest to clip the antennae into the bows, which saves trying to come up with a headband to mount them on. You can make them with pipe cleaners, black floral wire, or anything easy to bend into the right shape. They go straight up for about half the height of Cindy Lou's head, and then off to each side in scallops; spirals would give the right effect. The antennae will be the most fragile part of the costume, so don't be surprised if you spend a lot of time re-bending them. In fact, it may be easiest to only use them for pictures or the first few minutes of a party, and then just take them out.
And that's all there is to it. Anyone who's seen the cartoon will recognize your Cindy Lou immediately!