Your Akita may never accept the other dog so before you bring her into your home make sure you have a backup plan. Can you take the other dog back if things do not work out? To improve your chances, do your best to ignore the other dog when your Akita is around. If you show the new dog a lot of attention, you are more likely to make your Akita jealous, and she will dislike the other dog. After a few days, you will be able to evaluate how they are getting along.