She may just be getting used to breathing. Ds gave us some real scares a couple of times (one night we stayed up until 2 am watching him, because he was breathing funny, but he started breathing naturally and we went to sleep). Two thoughts, though.
First, do you produce a lot of milk? My cousin and I have both had this "problem" (if you can call it that). Our babies have just can't quite cope with all of it at first. They have to get used to used to it. One thing that helps with this is to only feed on one side at each feeding. Feeding on both sides at each feeding increases the amount of milk you produce, and if you've already got an abundant (or over-abundant) supply, you don't need that. Also, my cousin had to take her babies off when let-down started (she would have them latch on to get the milk flowing, but as soon as it was apparant that baby was getting a lot of milk, she would take him off) and either catch that milk or let it go to waste, and then put them on a minute or two later. That way they didn't get the rush of milk at let-down. And just know that babies do develop coping mechanisms for this. Some will learn to drink faster (and they get older they'll be able to cope with all of it without problem, but that may be months down the road). Others will learn to let some of the milk dribble out of the corner of their mouth, which can be messy (I always had to put a diaper below my breast to catch the excess milk), but is better than a choking babe.
The second thought is this. When she chokes while simply breathing, is after crying? Ds used to lose his breathing rhythm when he cried. Maybe it was because he cried so seldom and just wasn't used to it? He would make really scary gasping sounds.
Hope something here helps you figure this out. If you're really worried, you could take her to a trusted ped. or ask your midwife (if you have one) for advice and if this is within the realm of normal.