To be honest, I don't think the dog task was his only concern about Jenny, but I do think it was a concern. I will speak from personal experience, saying it takes a while to get someone who is not used to being around dogs to warm up to them to the point where they can actually act like the dog's owner. I never had dogs growing up, and most of my life I was always slightly nervous around them. I would still pet them if I thought they were cute, but it was always a bit awkward.
Two years ago, after my son's years of begging, we finally got a dog. He's a miniature schauzer/bichon frise mix, and I love him, but it took me a few months to actually get used to having him around all the time. It took living with a dog every day for all that time. Thankfully, my husband's family had owned dogs when he was growing up, and he was great with our dog, and he was able to help me adjust as well. Now, I am a lot more comfortable around all dogs, and it is not awkward to pet them or play with them. I noticed the change very clearly about six months after we got our dog, when I went to a friend's house and was immediately pounced upon (in a friendly way) by their large dog, and I didn't freak out one bit. I just laughed and patted the dog and then told him to get down, which he did.
Jenny, if she was cast in this role, would not be living with the dog 24/7 so it would probably take her longer to get used to having the dog around than it took me. It is a bit of a big deal. If you've never owned a dog or spent time with dogs on a regular basis, it can take a while to really get used to having one around all the time.
That's my thoughts about the dog task, but I also think that wasn't the only reason ALW got rid of Jenny. I don't think he ever saw her as Dorothy, and the dog task was just another reason to add to his list.
One side note about dogs--My favorite Toto on the show is Dangerous Dave, mostly because he reminds me of my dog.