Answer: Surprisingly, many common houseplants are in fact dangerous to pets. Banana is not included in the ASPCA's list of non-toxic plants.
I would therefore strongly suggest you check with your veterinarian for the most accurate information about plants that are toxic to dogs and make sure it would be okay. Puppies tend to get stomach aches and vomit and so on from chewing on things they shouldn't, so you might want to wait until the dog is older and over the chewing stage to be on the safe side for both the dog and the tree.
With regard to the banana tree, too, in my experience it is difficult to keep them healthy indoors without a greenhouse.
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