It will separate - kind of like curds and whey. If it really over-cooked, it is probably wise to feed it to the dog. In the old days, we would have slopped the hogs with our kitchen disasters. Nutmeg is the secret ingredient in eggnog. Custard is baked eggnog.
Purists use real rum or real brandy.
For health reasons, do not use real eggs for eggnog. Use egg substitutes because you can get very ill drinking a raw egg. This is not a low-calorie recipe. Firmer with the real eggs. Unsweetened chocolate, melted in the 2 Cups milk in a double boiler and beat smooth with a wire whisk before adding to sugar and eggs.