I would wait and see when that time comes, but if everything goes smoothly as it should, then I think that in your situation that it would be fine to get your puppy earlier than 12 weeks. If the puppy is eating healthily on its own and is completely weaned off mama, then the puppy should be safe to bring home around 7 or 8 weeks. Now, some people may disagree with me...this is just MY opinion. I brought both my babies home before 12 weeks...one at 7 weeks and one at 8 weeks. But, just because I did this does not mean it is the best thing to do. It is good that your cousin and you are so close because if anything DOES happen and you need to take the puppy back to its mama, then it would not be a big deal at all.
I bet you are SO extremely excited! Can't wait until your new baby is born. I'll be praying for a safe pregnancy and birth.