You will need to call Delta (DL) directly to book the seat. My daughter flies A LOT (She has one of the highest tiers of elite status on Delta) and has flown with us since she was 4 months old. On DL you will still need to pay for a lap child- generally 10% of the adult fare. However, you will also almost always get a discount for a child fare for international travel. For the cheapest fare classes you generally pay 75% of the adult fare. It can still be a lot but, a 25% discount really, really helps.

Yes, you can use an FAA approved car seat on take off, landing and through out the flight. In fact, if you have a car seat (and an airplane seat), the Flight Attendants, will likely demand that you use it during take off and landing.

Another option that hasn't been mentioned by anyone else yet is the Baby B'air. We have used this device many, many times. When my daughter was a baby and had a seat, we still brought it used it when she wanted lap time or when she wanted a snuggle. It is FAA approved for flying at cruising altitudes (though we have also used it during take off and landing- that is specifically not allowed, so I am not advocating that...however...). It will prevent your daughter from becoming a projectile should severe turbulance occur. In addition, and probably more importantly, it will prevent you from dropping her should you inadvertently fall asleep while holding her. I bought both of mine (they come in two sizes) used from Ebay or Craigslist. You could sell yours when done to minimize costs.

The Baby B'air has a nice video that demonstrates why you should use their product- in answer to your earlier question asking for more information about the potential hazzards.

I have seen severe turbulence that has thrown kids around on flights and also seen exhausted mothers drop their babies (one time I almost did it!!). For these reasons, even if the risk is remote, since the solution is so inexpensive I can't think of a reason not to use this vest. Note that while you could put your daughter in another type of harness (like the baby bjorn) this will not put her outside of your crush zone (YOU could crush her).

I don't think that anyone would argue that it would be more comfortable for your daughter to have her own seat, both for you and your daughter. And I don't think that anyone would argue that this isn't the safest way for her to travel in the event of the worst. However, there are alternatives that do provide some protection for her and are quite affordable.

You can always bring the car seat and ask if there are any open seats. That would certainly be nice. But, don't count on it- be prepared to not get one, and be happy if you do.

If you do buy a seat, be sure to enroll your daughter in skymiles. She will get quite a few miles for the trip.

Note that on Delta, even as a lap child, your daughter gets a baggage allowance:

•Children traveling on an international ticket that is 10% of the adult fare are allowed one checked bag up to 20lbs. (10kg) with a maximum outside dimension (length+width+height) of 45 inches, plus one checked fully collapsible stroller or push-chair.
•Children traveling on a ticket that is 50% or more of the adult fare, children are entitled to the standard baggage allowance.
•See Child Fares and Ticketing for Delta's current policy on special fares & discounts.