You said you have no idea how to explain that /oo/ is different from /o/. I would say that there really is no way to explain such concepts other than saying "two o's make an /oo/ sound." If that does not work then I would argue your DD is not ready for reading instruction. So, you need to wait for some maturation. I think typically this happens around 3 or 4. For your DD it might happen sooner. Who knows, she might puzzle it out by herself in the meantime.
I also want to ask if you think she is really obsessed with literacy, or if she is just enjoys learning things. Leaning letters and phonics was just another example of my DD's desire to learn things. I never really thought of it as an obsession with literacy. I took it an example of how good she was at rote memorization. More than that, I realized how much she seemed to enjoy memorizing simple information. When DD was your DD's age we taught her the planets and simple facts about each one. Now how different is that from learning the names of the letters and what they say? It is very similar. We have done the same with dinosaurs, continents, animals, states, presidents, crystals. Anything she showed an interest in, we have offered her something to learn. Each time we revisit these subjects, we expand.
I think that 99% of DD's "instruction" comes in the car, 10 minutes here, 10 minutes there. Our car is our classroom! Half the time we listen to music, and the other half I will just ask her what she wants to talk about. And, we go from there. We have gone over all her beloved interests in the car ad nauseum, and we also play word games like opposites, rhyming, phonics, and now spelling. That is it. That, and we read. A lot. About everything. Oh, and we play together.
Lastly, I would caution turning something so loved and special as reading a good book and turning it sour. (You don't sound like you would. ) It sounds like your DD loves book as much as mine. I'd recommend steering clear of early readers until she is actually reading. I would also recommend finding some really good long books to read together. I am a huge fan of children's literature done right. There are so many awesome books out there. But, for every one good book I find at the library I swear there are 300 hundred 'junk books'. The books we read these day last about 20 minutes each, and they are filled with rich vocabulary that would challenge some college students. Maybe, DD has learned to read a bit later because I didn't point out every word I said in those boring early readers every night, but I believe the benefits have greatly outweighed this cost.
DD just turned 2.5 and has actually only now shown some interest in reading things. She does seem almost ready for reading instruction. She does seem get that two Os say /oo/, that SH says /sh/, that doubling a letter really doesn't do anything, that you just need to know that 'the' says 'the'. What are we doing? I let her play with my iPhone for a couple of minutes in the morning while I sleep. I help her sound out words in her environment. I might point out some words I know she can sound out. Things will just happen. She has known all her state names for a while now, but is now wanting to match the names of the states with the puzzle pieces by reading their names. Of all things, state names! It has been the states that really seemed to have gotten her on a roll.
Your DD sounds amazing! You will find a lot of wisdom for yourself here on these boards.