This is just my opinion but I would wait until you can at least buy yours and your 10 year olds together. Sometimes planes do fill up (at least they do out of my airport - ATL) and it would be no fun if she has to take a seperate flight than you.
As far as seating, unless you are flying Southwest, I would think it would make it harder to select seats together too if you buy the tickets seperately. Although I guess if you pay for an aisle or window seat in advance, you have a good chance of getting at least being able to get the middle seat if you get your DD's ticket later so you could sit with your 10 year old at least.
If you are flying Southwest, pay for EBCI for each ticket and you'd be fine getting seats together I would think.
Good luck and have a great trip.