My fiance and daughter are American, I'm not... he wants to adopt my daughter

What is the name of your state? Indiana

Well, that's not entirely accurate. My fiance lives in Indiana, I'm in the Philippines.
My fiance is American, and because of my insurance (my father works in the foreign service) it was cheaper for me to give birth in the US than where my father was stationed (France), so my daughter is also a US Citizen. My fiance wants to adopt my now three year old daughter after we get married.(whose father is not listed in the birth certificate and from whom I never got any support, nor am in contact with) Will there be additional legal things that need to be done because I'm a foreigner, or will those hassles be negated when I marry my fiance?
My fiance already considers my daughter as his own, sending her presents, and talking to her via voice chat. She recognizes his voice and even calls him "Papa". She sees his picture and the photos of him and I together, and says "Is Mommy, is Papa." When we were together, my daughter allowed him to touch me (She doesn't let even my father hug me!) and would often make us kiss. My fiance adores her, always asking what 'our little girl' is up to, and is openly concerned about being able to provide for her. My family likes him, and have met him. We are just waiting until we are both finished with college to marry, and will tackle the legal hassles of an American wanting to marry a foreigner. We want very much to be able to complete our family!
Finally, my daughter was born in California. Which adoption laws will apply? The ones in Indiana, or the ones in California?

Thank you for your time,
Aurora