Can I use a passport number for my daughter? She doesn't have a SSN

A dependent must have either a Social Security number or an ITIN issued by the IRS.

You can apply for an ITIN or a Social Security number for her, but she cannot be entered on your tax return as a dependent until she has received the SSN or the ITIN.

As DoninGA explains, you must have an ITIN or SSN to list your daughter as a dependent.  Also, the IRS requires that the number be issued before the due date of the return (including extensions) for many types of credits.   

I would suggest that you file an extension, to allow more time to potentially meet that deadline.  You can file one within TurboTax or HERE.