You could always renew your daughter's passport early as they will add the unused months onto her new passport, then you need only do the one ESTA application and it will last 2 years - this would save time and money! [msnwink]

Ah, just re-read your post and it seems you have already done your ESTA - sorry! [msnsad]

And yes, you will have to pay to redo the ESTA when she gets her new passport.