Yes, there are likely fanfictions where Harry Potter calls Hermione 'baby'. Fanfiction writers often explore different relationships and character interactions in the Harry Potter universe, and this kind of endearing or unexpected use of language can be a part of their creative interpretations.
Voldemort's remaining followers could be antagonists. They might see the baby as a new threat or a potential weapon. They could try to kidnap the baby to use its power for their own dark purposes.
Another possibility is that they give the baby a name with a special meaning in the wizarding world. Maybe a name related to an ancient magic spell or a magical creature. For instance, for a boy, they could choose 'Phoenix' which represents rebirth and strength, just like the phoenix in the wizarding world. For a girl, 'Aria' which could be associated with a magical melody that has the power to soothe or protect.
Some of the more traditional pure - blood families might oppose it. They have strict ideas about family and bloodlines, and Harry and Hermione's situation doesn't fit into their narrow view. For example, the Malfoys might initially be against it, seeing it as a break from the 'normal' wizarding family structure.
Obviously, Ron and Hermione are the main characters as the baby's parents. Their personalities play a big role. Ron's humor and Hermione's intelligence are often passed on to the baby in different ways in the stories. Also, Harry Potter sometimes makes an appearance as the baby's godfather or just as a close family friend.
There might be a fanfiction where Ron and Hermione's baby gets into some sort of adventure in Hogwarts even at a very young age. For example, the baby might end up in the Forbidden Forest by mistake and befriend a magical creature there. This would add an element of danger and discovery to the story.
Another plot could be that the baby's existence somehow threatens the balance of power in the wizarding world. Some dark forces might want to use or harm the baby for their own gain. Harry and Hermione then have to fight against these forces, all while raising their baby in a world full of danger and intrigue.
It's not a common type at all. In the Harry Potter fandom, most fanfictions are centered around the well - known characters and their adventures, romances that were somewhat expected or their battles against the dark forces. The idea of Hermione breastfeeding Draco's baby is a very unique and not - so - often - explored concept in the vast sea of Harry Potter fanfictions.
One interesting fanfiction could be about baby Harry's first magical experiences even before he went to Hogwarts. Maybe he unknowingly made his toys levitate when he was really young, and his aunt Petunia was terrified but couldn't figure out what was really going on.
One possible story line could be that they discover they have feelings for each other later in life, after all their adventures at Hogwarts. They get married secretly and then have a baby. The baby might inherit some very unique magical abilities, a combination of Harry's courage - related magic and Hermione's intellectual magic. And they have to protect the baby from the dark forces that still lurk in the wizarding world, just like they had to protect themselves when they were young.