Can People Bless Their Pets?

A short article from the Summa Triviæ:

1.  It would seem that pet-owners cannot bless their pets, as it is an unheard of thing for masters to bless their slaves, and pets are to their owners as slaves are to their masters, even to the extent of their owners having the power of life and death over them. 

2.  Furthermore, it appertains to the priest to bless things for the use of men, and men must have recourse to the priest to have their own possessions blessed - so it would seem that if men's pets are to be blessed, they must be blessed by a priest; and all the more so because they are not inanimate objects, but have an animal soul, and so are higher than mere dead things, and therefore a greater virtue is needful to effect their being blessed.

I respond thus: It is indisputable that the lesser is blessed by the greater (Heb. vii, 7), and furthermore it pertains to the rights of the father of a family to bless his children with his paternal benediction, as all men know, and as the Scriptures testify - for so Isaac blessed Jacob (Gen. xxvii) and in his turn Jacob blessed his twelve sons (Gen. xlix); so it would seem that the owner of pets, that is, domesticated animals, may likewise bless them, since they are not as slaves to him, but as children - for, as the prophet Nathan told King David, there was a man who had a ewe lamb for a pet which "was unto him as a daughter" (II Kings xii, 3).

It will be seen that the first objection is thus met; and the second also, since pets are not so much chattels of men as like unto children - and they are the more like them in that they have a soul, though not a rational one.

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Questions, comments, from any scholiasts or disputants?