I have halved cake recipes before without issue. The most complicated thing to worry about is halving an odd number of eggs, but this question addresses that. The finished product was indistinguishable from the full recipe.
Edit
One thing to note. In your specific case, because it's a two-layer cake, halving is simple because you're only cooking a single layer. Halving other cakes, such as a pound cake, or a bundt cake involves adjustments to the cooking time. A halved cake will cook much quicker, and could possibly need a lower temperature as well as a decreased cooking time.
If the recipe calls for oil, butter, or any other fat, then you can try to scale the other quantities to match it.
If not, there's still a chance you can salvage it. The oil doesn't actually chemically react with the mix at all, it just "coats" it; in fact, most cake recipes use some amount of fat in order to slow gluten formation (i.e. stop the cake from getting tough and chewy).
However, if the recipe called for 1 1/4 cups water and you used the same quantity of oil instead, then that is going to be way too much oil for a single serving.
What I would do is double or maybe even triple the cake mix, make sure it's very well mixed with the oil, then add however much water you needed in the first place.
If you realized your mistake early (i.e. if the original recipe called for a lot more than 1 1/4 cups of water) then you might be able to just proceed as normal and end up with a very moist cake, but more likely you'll still need to add some more cake mix (and the corresponding amount of water) to compensate. I'd still double it, because otherwise you'll be stuck trying to figure out how to use the leftover mix.
Don't just add flour; the amount of water that the recipe calls for is proportional to all of the other ingredients in the mix, and it's virtually impossible for you to know how much extra water you'll need to compensate for the added flour. Besides, you'd only end up with a bland, flavourless cake if you did that.
If none of these options appeal to you then I'm afraid it's destined for the trash, unless you want to prepare your own cake mix from scratch and combine the two recipes.
Best Answer
Almost certainly yes, but the flavors will be slightly different.
Brandy is likely to be slightly more acidic than rum, but otherwise quite similar in composition, and should perform in the same way.
If you want a more tailored answer, you should provide more information, such as the full recipe.
See also: Are there any general principles of ingredient substitutions?