DALLE3 - How to turn real pet photos into replicas in different gestures and themes?

DALL-E is a diffusion model like Midjourney and Stable Diffusion.

Kinda. What it definitely does is reframe the prompt to be inline with OpenAI’s alignment efforts. Which is generally a good thing—when asking for a group photo of “doctors” it wouldn’t be appropriate for it to consist solely of old white men—but occasionally creates some hilarious goofs like trying to create ethnically diverse fantasy characters like “South Asian Dark Elves” @PaulBellow.

This is 100% correct. At least for now, DALL-E 3 doesn’t have img2img capability or inpainting so you’re not going to be able to get exactly what you’re looking for using this particular tool, unless your pet happens to look like the canonical example of a particular breed.