I would suggest a citrusy sponge cake (eggs, flour, sugar) topped with a little whipped cream or a light dusting of powdered sugar. Martha Stewart has a good one on her website:
http://www.marthastewart.com/340377/vanilla-sponge-cake

Just add zest to the batter.

We do creme puffs - a joy of cooking cream puff recipe with a chocolate ganache (one bag of chocolate chips melted in whipping cream, chilled and whipped).

Delicious and light (or lighter).

I know how you feel. My son turned two on November 29th and I made him a sticky toffee "pudding" cake (the British call all desserts puddings, the recipe is from Ireland). The recipe is absolutely delicious with the caramel sauce that they suggest, and we cut out a "2" stencil and put it on top of the cake while we shook powdered sugar over, so that the cake said 2 when we took it out to my son. He loved it! I always get requests for the recipe when I make it.
http://www.epicurious.com/recipes/food/views/Sticky-Toffee-Pudding-104071
I use all-purpose flour plus some baking powder and salt to substitute for self-rising (you can find the substitutions online). Also, I have found a half recipe of the caramel sauce to be sufficient. Happy birthday to your daughter!

I made this cake for my daughter's first birthday
http://www.foodnetwork.com/recipes/paula-deen/banana-nut-cake-with-cream-cheese-frosting-recipe/index.html

Minus the nuts, of course. I'm a "cake from a box" kind of gal myself, but this was easy to make and was honestly, amazingly delicious.

One of my FAVES:
http://allrecipes.com/recipe/mandarin-orange-cake-i/

I do sub things to make it less sweet (the fruit really is all I need). I use a no-sugar homemade cake base (you might wish to just not add the full amount), and use everything else. We did do real whipped cream once, heavier but awesome!

Citrus flavors or fruit flavors. A bundt, while not super fancy looking, is a much cleaner light tasting option. A tres leches cake would be nice too.

Though I must say, as a December baby close to Christmas, I'd encourage you too loosen up on wanting her birthday to be really different from the holidays. So long as she isn't re-gifted a early Christmas present as a birthday gift (cardinal sin for a Dec birthday!) I'd see as she gets older her thoughts on it. From my years of meeting others with birthdays now, most seem to agree that we LIKE Christmas themed birthday cakes and stuff like that. I always have.

I can't think of any recipes in particular, but you may want to investigate vegan cakes, which are often lighter due to their lack of butter. Sometimes they just trade animal fat for vegetable fat, but many recipes are healthier.

Alternatively, what about making a regular recipe but miniaturize it (mini-cupcakes)? My personal philosophy with cake is not to compromise the sugar and butter and chocolate, but just to eat less of it. It sounds trite, but it works if you stick to your intention to eat less.

I'm a June baby and don't like heavy cake in the summer, so I usually go with a tart or a pie. My friends think I'm silly.

There's a *wonderful* buttermilk cake on Smitten Kitchen that I make ALL the time in the summer, because it's esp. good with berries and other summer fruit: http://smittenkitchen.com/2009/05/raspberry-buttermilk-cake/
But for this time of year I imagine it could also be wonderful with cranberries (and orange zest!). It only has half a stick of butter (it's a fairly small cake), and comes out very light and fluffy. And a snap to make.

Buttermilk cake or banana cake from the Cake Bible are both less sweet options. The buttermilk is wonderful with berries and whipped cream. The banana cake is fine on its own but great with a thin layer of chocolate ganache (skipped for the birthday girl).

I've made this cake from Cooking Light a couple times, and it was really good:

http://www.myrecipes.com/recipe/white-birthday-cake-with-italian-meringue-icing-10000001054822/

A classic French yogurt cake, i.e. "gâteau au yaourt," is not too sweet and so simple to make.

Here's a recipe from Clotilde of C&Z -- you can use less sugar than she does if you want!

http://chocolateandzucchini.com/archives/2005/10/yogurt_cake.php

here are a bunch of healthy options, I made an applesauce/banana cake with no added sugar for my twins 1st bday, I did use sugar in the cream cheese frosting though.
http://wholesomebabyfood.momtastic.com/tipFirstBDay.htm

This Lemon Thyme Cake is great http://www.thekitchn.com/thekitchn/dessert/lemon-yogurt-cake-with-gingerthyme-syrup-109936

My daughter's birthday is right after Christmas, and this year I'm planning to do a gingerbread cake with whipped cream frosting, with some orange zest on top.

I made an olive oil cake once for a dinner party and everyone loved it!

I understand your dilemma! My son was born on New Year's Day. By that point in the holiday season all the family is pretty feasted-out. But, for his 1st bday last year I did still make a carrot cake. I used half whole wheat flour, but back on the sugar, but still wanted to have a traditional birthday cake. And all those relatives who were holiday-ed out still ate up the entire cake! Cupcakes would probably be a good option too. Not light exactly, but small portions. Otherwise, I like the idea of something lemony. Ina Garten has a great lemon pound cake on the food network site, if you don't mind the loaf cake look. Good luck!

Thanks for the ideas, everyone! I'll decide closer to her birthday (but she does love citrus, so...).

Ooh, banana cake, definitely. That would be perfect for little ones and adults alike, and a simple glaze takes it from plain to pretty.

There's a great clementine cake out there, originally made by Nigella Lawson, it only has a few ingredients whole clementines, eggs, sugar, ground almonds, and baking powder. Dress it up with some powdered sugar and clementine segments and it should be very pretty, plus it tastes absolutely amazing.