What harm (emotional harm) could come to a child who wants to pretend, in play, that they are a cat or a dog?

I have a five year old daughter and we also have cats and some aquarium pets. She loves dogs and wishes we could have one, but we’re not home for long stretches and so I think she understands it would not be practical.

I am a pretty laid back parent. Other than something that causes her physical harm, there is little she is not allowed to do (she is not allowed to write on walls or furniture, which she has never tried to do, and sometimes I will reprimand her if the house is clean and she starts making a mess). She is a good kid and everyone from teachers to babysitters have said how good she is.

One thing she likes to do in pretend-play is pretend she is a cat or dog. She crawls around on the floor, wants to be walked (crawling on floor with a leash on), or may pretend she’s an injured animal going to the animal doctor. She sometimes will do this with her stuffed animals, doctoring them, and sometimes she is the animal, needing medical care.

Yesterday at my mom’s house, she started doing that with a family friend who was visiting. My mom told him not to allow that and I heard her saying something to him in the living room. My mom told me later that she told him that one day she went to pick up my daughter at school and the kids were playing “house” with one kid as the mom and one kid as the dad, and my daughter was the dog, crawling around on the floor. My mom, who was in college in the 1960’s, told me she recalls sorority hazing rituals that were similar and she doesn’t think it’s good for the child’s self esteem to pretend she is a dog.

I am wondering what other Jellies think of this. Can it be harmful to allow a child to pretend she is a dog or cat?

I am asking this in “General” because I want to avoid the jokes and silly comments that are often in “Social.”