Yes, according to the American Speech-Language-Hearing Association (ASHA), diagnosing and treating delayed literacy skills is within the scope of practice of speech-language pathologists.  https://www.asha.org/policy/sp2016-00343/

Speech-language pathologists (SLPs) play an important role in the literacy development of children as they can provide assessment and treatment of written language disorders in addition to oral language disorders.  SLPs have specialized knowledge about underlying language skills that are related to both written and spoken language.  Foundational spoken language skills impact children’s development of reading and writing abilities.  Because spoken and written language are connected, children with spoken language difficulties often have difficulty learning to read and write.  Therefore, it is important that a speech-language pathologist be consulted not only when a child has delayed spoken language, but also when a child is having difficulty learning to read.  Underlying language deficits may be impacting their progress and SLPs are uniquely qualified to assess and treat if necessary.