Do I need to file my daughter's taxes first, or DO I file my taxes first? I will still be claiming her as a dependent. Thanks

They are two separate returns.   One has nothing to do with the other.   So the order you prepare them in or file them in does not make a difference.     Each return needs its own account.  Do not use the same account and user ID or the second one will overwrite the first one and it will be lost forever.

MY DEPENDENT HAD A JOB

If your dependent has a W-2 for his after-school job, summer job, etc. you do not include the information on your own return. You can still claim your child as a dependent on your own return.  He/she can file his own return for a refund of some of his withheld wages (he won’t get back anything for Social Security or Medicare), but MUST indicate on it that he can be claimed as a dependent on someone else’s return.  (Supervise this closely or prepare it for him!)

If your dependent’s earnings were over $400 and were reported on a 1099Misc or 1099NEC then he must file a return and pay self-employment tax for Social Security and Medicare.  You may want to use this version of TT for that:

https://ttlc.intuit.com/questions/1900583-what-is-turbotax-free-file-program