S.S.
Hi H.,
I've flown nearly 10 times with my now 16-month-old and it's all gone pretty well. Sometimes I go it alone and sometimes I go with my husband. In any case, we usually manage with one suitcase (when it's just my son and I), the pack-and-play for him to sleep in and his stroller/car seat. Fortunately this trip home my parents kindly bought a car seat so I wouldn't have to cart the large one home, too.
You'll need to bring extra diapers in case of layovers and delays. Extra food (if she's eating finger foods). If she will take formula, it might be good to have a little on hand for back-up. I've always been lucky at airports and they've let me bring bottles of milk or breast-milk or made-up formula through as long as I bring them out and show them to security. Also, hand sanitizer is good to have, along with a couple of small toys to occupy your little one and maybe a blanket. One of the most invaluable things I've brought along is a carrier or some sort (the baby bjorn when he was younger, the ergo now). It allows me to be hands free when I'm getting onto the plane (you can bring the stroller right to the plane, by the way) and also when my son falls asleep it allows me to read my book, watch movies, eat, etc. in comfort.
I think when you fly really depends on your daughter's schedule. We take early flights when I go home, which means he'll nap on me for most of the way (still! Thankfully!). Evening flights near bedtime are also good as he tends to fall asleep on me as well. He almost sleeps better on the plane than at home! A red-eye should be fine, but might be looong just to go to Detroit. I fly to Toronto regularly and try to go direct as it is four and a half hours and that's been fine so far. (Detroit's just south of Toronto, Canada, so should be the same length of time).
Anyway, happy travels!