AAGH! BLOODY TRAVEL AGENTS!!!
SOME countries require a minimum period of validity on a passport when you enter (or plan to leave) their country. Rather than train their staff properly, many travel agencies tell their staff to (incorrectly) instruct customers that ALL countries have that rule! (GRRR!!!!)
The USA DOES have a '6 month validity' rule for visitors from MOST countries but there is an agreement with the UK government that means that the rule does NOT apply to holders of BRITISH passports.
Do NOT believe the travel agents. Instead put your trust in this answer from the website of the United States Embassy:
http://london.usembas...passports.html#niv079
If you do decide to renew your daughter's passport anyway, she will NOT lose any period of validity. Whenever you renew a British passport, any unexpired period on the old passport is automatically added to the validity of the new one (up to a maximum of 9 months). So, if you were to renew your daughter's passport in September, her new passport would be valid for 5 years 6 months.
Chris