Yes you will need to get a travel permit (Form I-131). You will not have to purchase it if it is filed concurrently with your I-130/I-485 application. You or your daughter may want to work with an immigration attorney as immigration law can be quite complicated and small mistakse can sometimes lead to delays or denials. An attorney can help prevent these or deal with them if they do occur.
Andre Olivie, Esq.
Seattle Immigration Lawyer
Anyone applying for travel documents likely will get them since USCIS only check whether the applicants meet the requirements stated on the form. USCIS does not check whether the applicants would be not admitted back into the US.
For some applicants of adjustment of status, traveling outside the US, even with travel documents, may result in not being admitted back into the US. For example, applicants who accumulated enough unlawful presence in the US are not admissible. Once those applicants leave the US, even with pending petitions for adjustment of status, the applicants would not be admitted back into the US.
You should review with your attorney whether you have any ground that would render you inadmissible. Some grounds, such as unlawful presence and working without authorization, are generally not held against immediate relatives of US citizens as long as the applicants do not leave the US before being granted legal permanent residency.