One common theme is the exploration of family. Since the Doctor and Clara having a baby is not a typical situation, it often shows how they redefine family. Another theme is the protection of the baby from various threats in the Doctor Who universe.
It could be all sorts of things. Maybe Clara has to protect the baby from some alien threat or it could be a story about her raising a time-traveling baby.
The Doctor's friends from different planets or time periods might react in unique ways. For instance, some alien friends might see the baby as a symbol of hope for a new alliance between different species. Others might be a bit afraid of the baby's potential power and try to keep their distance at first, but as they get to know the baby, they warm up to it and become protective.
The plot might be centered around how the Doctor and Clara adjust to their new roles as parents. For example, Clara could be worried about how the Doctor's long absences due to his travels will affect the baby's upbringing. And the Doctor might be trying to find ways to balance his life-saving adventures with being a good father.
One great 'doctor and clara baby fanfiction' is 'A New Beginning'. It beautifully explores the Doctor and Clara's journey into parenthood, with lots of heartwarming moments and their unique adventures while raising a baby in the TARDIS. It's full of the typical Doctor - Who - esque charm and wonder.
It could be for creating drama and tension in the story. Maybe it adds a new layer to their relationship or drives the plot forward in an unexpected way.
One of my favorite moments is when they face a seemingly impossible foe in fanfiction. Clara's quick thinking and the Doctor's knowledge combine to outwit the enemy. It shows their great teamwork.
Well, a prevalent theme is exploration. They explore new planets, civilizations, and time periods. The theme of trust is also big. They have to trust each other in all the dangerous situations they get into. Additionally, there's the theme of mystery. There are often things about Clara's past or the Doctor's true nature that are mysterious and the fanfiction tries to explore that. For example, in many stories, Clara's real identity or her connection to certain events is a mystery that gets unraveled slowly. It adds an extra layer of intrigue to the story. And of course, the theme of heroism, both Clara and the Doctor showing courage in the face of danger.