9 months? You don't have to worry about a baby showing up until at least 11 months gestation, some donkeys even hold on until 13 months (gestation period is longer in donkeys than horses). So I wouldn't worry about straw at this point, just use shavings.
When she gets closer, or when she starts to bag up, you can put a layer of shavings down with straw on top. When you clean it you can fork out all the soiled straw, but most of the urine will go through it. You can then fork the straw that's still good to the side, and clean up and replace the wet shavings. This way it's much easier to keep the box clean.
I don't think it's so much suffocation you worry about as the dust from the shavings. Straw has much less dust than shavings, and having a layer or straw on top will help separate the foal from the dust, and help keep dirt out of his umbilical stump.