Try The Child Development Centre Qatar who have pedo speech ,physio , occupational and educational therapists.They have a facebook page .
Freelancing therapists can be found through a group called Out of Sync Network Doha .
https://www.bigtent.com/groups/outofsync
Be aware that you can not claim on insurance using freelancers as they aren't registered officially.
My family will be moving to Doha in the next few months. My son is 3 years old and is delayed in speech. Does anyone know any Speech Therapist or Speech Therapy Clinics? Thank you in advance. K