Optical fiber sensors have been validated for physiological measurement as a potential device for smart textiles and wearable sensors. Also, developing sensors with Polymeric Optical Fiber (POF) shows promising applications in dynamic and real scenarios, as low-cost alternatives. Furthermore, the functioning of POF sensors can be used in no-skin contact applications, such as in highly skin-sensitive children with Autism Spectrum Disorder (ASD) during therapies. On the other hand, Dog-Assisted Therapy (DAT) is a stress-reducing method and has been studied to identify its influence on improving therapies and stress-related events. This work presents a case study in three weekly DAT sessions focused on speech therapy in a subject with ASD. A validated low-cost POF sensor was used in this first dynamic physiological measurement scenario. The analysis of five Heart Rate Variability (HRV) variables was made to compare the participant's physiological status before and during the DAT. The obtained pulse signal showed the dynamic movements affecting the signal but being able to obtain the pulse peaks. The physiological comparison showed a difference in the mean peak-to-peak time interval when the child was interacting with the dog than previous to the interaction in Session 1 and Session 2 (p-value<0.05). Also, an improvement in phonological consciousness was obtained, increasing by eight points after the three weeks of therapy. This case study showed the potential use of POF sensors in dynamic environments, and for wearable or smart textiles for children with ASD.