Well, while Clara and the TARDIS are central, there could also be mentions of the Doctor in the fanfic. Even if it's mainly about Clara and the TARDIS, the Doctor's influence is likely to be felt as he is an important part of Clara's journey and the TARDIS's existence.
Obviously, Clara and the TARDIS are the main characters. Clara, with her inquisitive nature and strong will, and the TARDIS, the sentient time - space ship with its own mysteries.
One interesting plotline could be Clara discovers a hidden chamber inside the TARDIS that contains secrets about the Doctor's past. Maybe it holds memories or artifacts that the Doctor has long forgotten or tried to keep hidden.
Obviously, the main characters are the Doctor and Rose. They are the ones who go into the wrong Tardis.
One main idea could be the combination of different fictional universes. Harry from one and the TARDIS from another.
It could be an adventure where Clara and the Tardis Little One face some unknown threats together.
There could be some original characters created specifically for the fanfic. For example, a healer or a midwife type of character who helps Clara during her pregnancy. And then there are the allies they might have made in their previous adventures. These characters could come to their aid when they face difficulties related to the pregnancy, whether it's protecting them from enemies or just helping with day - to - day tasks.
A really interesting 'Doctor X Tardis' fanfic I've come across is 'Tardis Tales'. In this fanfic, the Tardis has a sort of consciousness that the Doctor tries to fully understand. It delves into the mystery of the Tardis' inner workings and how it has a connection to the Doctor on a deeper level than just being a ship. It's a short but engaging read that will make you look at the Doctor - Tardis relationship in a new light.
I'm not sure specifically as I haven't read this fanfic. But generally, if Harry is related to the TARDIS in a fanfic, it might involve some sort of crossover where Harry from the Harry Potter universe has an encounter or connection with the TARDIS from Doctor Who. It could be a really creative take on combining two very different fictional worlds.
Since I don't have first - hand knowledge of this fanfic, my best guess is that it could involve a situation or concept that is more 'blue' in nature compared to the TARDIS. Maybe it has to do with a different kind of blue - hued alien or a blue - tinted dimension that is explored in the story. It could also be a play on words, where 'bluer' refers to something other than the color, like a 'bluer' state of mind, and the story then weaves this concept in relation to the TARDIS, perhaps showing how this 'bluer' thing interacts with or is different from the TARDIS.
Obviously, Clara Oswald herself is essential. She is the main character associated with the baby. Then, the Doctor could be a great addition. His relationship with Clara could add depth to the story, especially when it comes to how he reacts to the baby. Also, Clara's friends like Danny Pink could be included. His presence could create some interesting situations regarding the baby, like how he might act as a father figure or a protector.
The main characters are Clara and Davie. They could be a couple, friends, or siblings. In a historical context, if it's set during a war, they might be soldiers or civilians trying to survive. For example, if it's a World War II - based story, they could be resistance fighters or people trying to keep their families together during the bombings and shortages.