C.,
I am new at the whole daycare thing, but when it comes to carseats I either find cheap/safe ones at garage sales or I ask the parent to leave one with me.
You never know when one might come in handy, so I would bring it up with her. She might even have one that you aren't aware of.
If such an occurance were to happen, I would pack up the remaining and possibly the sick/injured child and drive to the hospital. If the ambulance needed to be called I would most likely meet the child at the hospital with the other children. That way if the parents of the other children can't come right away I still have transportation for them. Also I have transportation back home once the family of the sick/injured child shows up at the hospital.
Sending the child alone in the ambulance isn't the best option out there by any means, but unless that's the only child you're watching at the time there aren't a lot of other options. But regardless of how I went there I would get back to the child asap.
Every daycare has different methods, but the bottom line is whether or not your child will be taken care of. She may have too many kids to 'transport' which means she needs to have a backup person so she can ride in the ambulance etc. I only care for up to 3 kids, so regardless of what happened, all the kids would be taken care of.
K.