Maybe they travel back to the time of the First Men. They have to learn to survive in a more primitive world. Daenerys could use her leadership skills to form alliances with the First Men tribes, while Jon, with his knowledge of the future, tries to introduce certain concepts like basic medicine. Their relationship could develop in a different way in this new and challenging environment.
They could be sent back in time by some magical force right before the events of the show start. They then have to work in secret to change things. For example, they could find a way to stop the White Walkers from being created in the first place. This would involve a lot of sneaking around and using their wits, and also exploring their feelings for each other in a whole new context.
One idea could be that they travel back to the time when the Targaryen dynasty was at its peak. Jon could see Daenerys in her element as a Targaryen princess. They might try to change some of the events that led to the downfall of the Targaryens, like preventing the Mad King's actions. But this could have unforeseen consequences for the future they came from.
Well, a simple idea could be that the pregnancy is a secret at first. Only a few close allies know. Jon and Daenerys have to be very careful to keep it that way. They might have some close calls where the secret almost gets out, adding a lot of tension to the story.
One idea could be a story where Aemon grows up in a world trying to heal from the previous wars. He has the combined traits of Jon and Daenerys, being both strong - willed like his mother and having a sense of honor like his father. He could be on a journey to discover his own place in this new world, facing challenges from those who still hold grudges against his parents' union.
There's 'Time Traveling Dragons' which is an interesting take. They are sent back in time to a period where dragons were more common. Daenerys gets to see how her ancestors interacted with their dragons, and Jon is there to support her. The story has a lot of twists and turns as they try to find a way back to their own time while also changing some things in the past for the better.
In a time travel fanfiction, their son could go back to the moment when Jon and Daenerys first met. He could subtly change their initial interactions to make them trust each other more quickly. This could lead to a stronger alliance from the start. He could also travel to the times when they faced their biggest challenges individually and offer solutions. For example, when Daenerys was dealing with the slavers in Slaver's Bay, he could give her ideas on how to end slavery more effectively and gain more loyal followers, which would have put her in a better position when she reached Westeros.
Well, in some fanfictions, the baby could be a symbol of hope. As Jon and Daenerys' child, it represents the union of two powerful houses. The baby might grow up to be a great leader, trained in both the ways of the Targaryens and the Starks. It could bring about new laws and a more just society, learning from the mistakes of the past rulers in Westeros.
One idea could be that Jon and Sansa travel back to the time before their family's downfall. They could then use their knowledge of future events to prevent Ned Stark's execution. This would completely change the course of the story and they might be able to save many of their family members.
One plot idea could be that in a world where their genders are swapped, they still have to face the same political challenges. Female Jon, with her Stark honor, and male Daenerys, with his Targaryen ambition, form an alliance that slowly turns into a romantic relationship as they realize they can achieve more together. Another could be a scenario where they meet in a different setting, away from the main events of the original series, and their relationship develops from there.
One idea could be that the baby is born with a special ability, like being able to communicate with dragons even more so than Daenerys. Maybe the baby's presence unites the remaining kingdoms in a way that Jon and Daenerys alone couldn't. Another thought is that the baby becomes a symbol of hope for a new era, with people from all over coming to see the new heir of the Targaryen - Stark line.
One interesting idea could be the political implications of their baby. Since Jon and Daenerys both have claims to the throne, their child would be a powerful heir with a complex lineage. Another idea might be the cultural impact. Their baby could symbolize a union between the North and the Seven Kingdoms, bringing different traditions together. Also, the baby could be a key factor in uniting the remaining factions after the great war, as it represents a new hope and a future for the war - torn land.
It could also develop more complicatedly. Suppose they travel to a future where one of them has made a big mistake in the fight against the Night King. This could create mistrust or a power struggle between them. Maybe Daenerys blames Jon for something that went wrong in the future battles, and they have to work through that while still trying to deal with the Night King threat.