There's a solution to that, too. It's called "common law name change." My kids used my last name from early on. It wasn't official but, eventually, schools accepted it. At some point the SSA issued cards with my name and, eventually, they were able to get driver licenses. From then on nobody ever asked for court papers.
Try it. Your daughter is old enough to be able to politely insist that she be referred to by your husband's last name informally and still use her old name where it's officially required until the change is accepted. When she's 18 she can go to court and make it official.