As long a your budget allows it, I'd strongly recommend purchasing 2 seats. Flying TCON with a 9 month old is hard even under the best of circumstance. If your daughter is a lap child, your wife should be prepared for the (likely) outcome that the plane is full and she has a toddler on her lap for 6 hours.

If you get 2 seats, I'd also recommend taking your infant carseat onboard (so your daughter can nap in it). A convertible carseat should be possible too, but not as easy.

Be aware, though, that a rear-facing carseat can make it impossible for the person in front of you to recline. And if your kid kicks, that will make the carseat bang the person's seatback. I think, but am not sure, that you can avoid this problem, by getting seats in a bulkhead row.

For more tips you should check out the flyertalk forum for travelers with children.