The common word used to refer to a dog of either sex in everyday English today is "dog". Native speakers of English don't usually use sex-specific terms nowadays when speaking of individual dogs. They say, for example, "my dog", not "my bitch". "Bitch", if not used derogatorily, is a technical term used mostly by dog breeders. But was that different in Victorian England?
Whatever terms were commonly used by dog owners in the nineteenth century should frequently appear in books of that time, so we can look in books to find out about the usage. To differentiate other mentions of dogs (e.g. by breeders or dog haters) we can look for phrases such as "my dog", "my bitch", "my doggess", etc. So what we can do is look at the frequency of these phrases or ngrams. Fortunately, Google has digitized many books and offers a free public tool that allows us to search books for these ngrams, the Google Ngram Viewer.
As you can see, the most frequent ngram during the ninteenth century is "my dog":
"My bitch" and the other synonyms for dog are rare, and there are no results for "my doggess" at all. This seems to indicate that dogs were commonly referred to by dog owners as "dog" – or probably, like today, by the dog's name.
The Collins Dictionary tells us that "doggess" is a humorous term. The word doesn't even appear in most other dictionaries. As such, we shouldn't expect it to be commonly used by dog owners to speak of their dog.
I showed you an easy way to do this kind of research using publicly available tools. If you wanted to be more thorough, you would use more comprehensive tools such as the Oxford English Dictionary (OED) that tells you when what word was in use and with what meaning and give you historic examples for the different kinds of usage. There you could verify or falsify if your word was used in the way you want to use it in a certain period.
Most university libraries and many large public libraries have bought a license for the OED and you can access it from computers in the library network. If you write historical fiction, you likely need to research other things as well. You could wait until a couple of research questions have accumulated and then spend a day at the university library to do your research.
In the OED all the quotations under doggess are from humorous publications. All the quotations under bitch (with the meaning of "female dog") from the 1800s are in relation to breeding.
The relation between dog owner and dog was probably different in the Victorian era than it is today. Here is an introductory article about the development of pet ownership during that time: https://www.theguardian.com/lifeandstyle/2019/oct/19/pets-how-victorians-turned-beats-into-mans-best-friends. And here is a review of a book on dogs during Victorian times: https://www.cam.ac.uk/research/news/how-the-dog-found-a-place-in-the-family-home-from-the-victorian-age-to-ours