Do I Need To A Us Passport For My Child When Entering Back From Japan Or The Philippines?

Me and my 3 month old are planning to travel to the Philippines/Japan in a week or so, due to family emergency. I am a green card holder and a Japanese Citizen. My daughter was born here and she has a birth cert and a SSN. Will she need a US passport to enter back in the US? Can she use her Japanese passport instead to enter back in the US? How long does it take?