My short answer to this is, Yes. I think it is both the teething and the birds that are waking her.
I don't really have any major words of wisdom or advice for you, I'm afraid - I always look forward to the time shifts, both spring and winter, purely for the impact on bed time / awake time (we always want it different from what it actually is - lol!).
Does your DD stay in her crib / cot / bed happily when she wakes early? Or does she shout / cry for you? If you think she might stay in her cot with some toys / drink of water / books / snack etc in the early hours, even if just for another 30 mins or so to give you a little bit more sleep, is there anything you could rig up that would help her - e.g. when you go to bed, sneak in with some toys / books / drink / snack and put it at the bottom of her bed to find in the morning?
If not, given that you are pregnant, the only other thing I can suggest is that you shift your body clock to go to bed even earlier than you currently do (which is probably quite early anyway - I remember what it felt like to be pregnant!) and forget all and any housework etc for the time being.
ou could try walk in / walk out (tiring when you are pregnant) / gradual withdrawl / double heavy duty blackout blinds / white noise etc etc, but if her teeth are waking her, then there is not an awful lot I think you can do - just make sure she has pain meds and try and get as much sleep as you can when you can.
Your DD is getting about 12.5 hours sleep in total in a 24 hour period - she can definitely survive on this much for a good few weeks / months.
Poor DD and poor you - it will get better, promise! Wishing you the best through your pregnancy.