She could travel to different alternate timelines. For example, a timeline where Danny never became a half - ghost. Dani's presence in such a timeline could cause all sorts of chaos as she tries to figure out how to get back to her own timeline while also dealing with the differences in this new world.
Dani might time travel to an era in the Danny Phantom universe's past where ghosts were more powerful or had different relationships with humans. This could lead to her having to form alliances with ancient ghosts to solve a problem that is affecting her own time.
One possible story could be that Dani travels back in time to prevent a major disaster in the Danny Phantom world. Maybe she goes back to the time when the portal was first opened and tries to stop it, which would change the entire course of events in the series.
One idea could be that Danny and Sam travel back to the founding of Amity Park and accidentally change something small that has huge consequences in the present. For example, they might stop the first settler from building in a certain spot, which then changes the layout of the whole town and where ghosts can enter from in modern times.
One idea could be that Danny and Ember accidentally travel back to the founding of Amity Park. They could witness the early settlers dealing with strange ghostly phenomena and have to figure out how to not disrupt the timeline while also helping the settlers. Another plot could be that they travel to a future Amity Park that is overrun by a new type of ghostly threat, and they bring back knowledge to prevent it in their own time. Or they could travel to a time when Danny's parents were kids and see how their obsession with ghosts started.
Another possibility is a time - travel fanfiction. Danny and Dani accidentally travel back in time and have to figure out how to get back. Along the way, they meet younger versions of their friends and family and have to make sure they don't change the future too much. This could explore their relationship in a different setting and also show how Dani's powers might be different in the past.
One interesting Danny and Dani fanfiction could be about them teaming up to fight a new and powerful ghost. They use their combined powers and unique abilities to outwit the enemy. For example, Dani might use her speed while Danny uses his more powerful ghost ray.
Maybe Dani is not really Danny's clone in the way they thought. There could be some other mysterious force or entity that had a hand in her creation, and as they dig deeper into her origin, they find out that she has a much greater destiny than just being Danny's 'daughter' in a sense. This would completely change the dynamic of their relationship and the direction of the story.
One idea could be that Danny discovers a new ghostly power that he uses to take revenge on a group of bullies who have been tormenting his friends. He could use his intangibility in a creative way, like sneaking into their lockers and making their things disappear.
One idea could be Danny Fenton having to deal with a new ghostly enemy that can manipulate time, making his double life as Danny Phantom even more chaotic. Another could be Danny trying to balance his high school life, including exams and relationships, while also facing a ghost invasion that only he as Danny Phantom can stop. Or perhaps a story where Danny Phantom discovers a hidden power within himself that has a connection to his human side, Danny Fenton.
One possible plot could be that there's a school talent show. Danny and Dani both decide to enter, but they want to keep their singing abilities a secret from the other because they're not sure how the other will react. As they practice in secret, they start to discover new things about themselves and their powers through the music.
One idea could be that Danny gets an illness that affects his ghost powers. For example, he might start losing control over his intangibility or invisibility. This could lead to some really comical or dangerous situations. Another idea is that his friends try to find a cure for his strange ghost - related illness while also keeping it a secret from the town.