Googling the two terms in Japanese, there are a great deal of discussions among the Japanese about when to use which as clearly ambiguous to them as much as it is to you. One of such quoted the definitions from Dictionary of How to Count (『数え方の辞典』) written by Asako Iida (飯田朝子).
More or less the definition of "小型の爬虫類、両棲類" for 匹 seems suited for this case. One may say it is an expression of belittlement. But also it can be taken as an expression of endearment by the diminutive expression.
One of the discussions said NHK does not have clear definitions in use of the two terms and neither for average native Japanese speakers. Some says, 頭 is used for any animals large or small in zoology. Some suggested that there is some historical legacy in native speakers count in some unit the way they do (e.g. rabbits counted as 羽 so that Buddhists who was forbidden to eat 4 legged animals can eat it as birds). Some says 匹 is used for hunting, distancing hunters from respecting the games.
All in all, we can read in a lot and try to see meanings behind it. But I am not sure if the authorial intent can be clarified in a clear cut manner here. I, as an average native Japanese speaker, certainly can't.