Eggnog Rice Pudding

I just completely made up a recipe for rice pudding - here it is in case it's good (we had an assload of cooked white rice left over from Chinese takeout last night.)

Rice Pudding:
5-6 cups white rice, cooked (!)
1 cup cream
3 eggs
6cups or so milk
1/4 cup or a little less Captain Morgan's Spiced Rum (I don't know why, it just seemed apropos)
splash of lemon oil
healthy dashes of cinnamon and nutmeg
about 1 to 1 1/3 cups brown sugar (which I forgot to put in until just now, when I was typing it out! I had to pull it out of the oven to add it.)
And also I sprinkled the top with white sugar in hopes that it would get a little crusty and nice.

And it's in the oven at 300. I didn't bother with no stinking bain marie, so I'm just going to bake it for 1 - 1 1/2 hours in there. Sure does smell good.