There could be. Fanfiction is a vast world, and fans often come up with unique and sometimes unexpected storylines. Beast Boy and Starfire are both popular characters, so it's not unlikely that someone has written a fanfiction with this plot. But it might be hard to find among the countless other fanfictions.
Another storyline could involve her friends' reactions. Her teammates might be overly protective, like Robin being extra vigilant about her safety. They could also be helping her with things she can't do easily during pregnancy, like heavy lifting or flying long distances if it becomes too strenuous.
One possible theme could be responsibility. Beast Boy would have to face up to the fact that he is going to be a father, which is a huge responsibility. Another theme might be acceptance within the Teen Titans team. They would need to accept this new situation and support their friends.
It can change the team dynamic in many ways. For starters, the team will become more protective of Starfire. They may take on more of her usual tasks to ensure she is not overexerting herself. This could lead to some characters developing new skills as they fill in for her.
One possible plot could be that Robin and Starfire's relationship deepens over time. They might face challenges from their superhero duties and public scrutiny. The pregnancy could then add more complexity, like how they'll balance their lives as heroes and soon - to - be - parents. Maybe they'll have to deal with villains who try to take advantage of Starfire's condition.
One great fanfiction in this theme might be about how Robin and Starfire handle the news of the pregnancy. It could explore their different reactions. Robin might initially be in shock but then quickly turn into a protective mode. Starfire, on the other hand, could be overjoyed and full of anticipation.
One possible aspect to consider in 'Starfire Gets Her Period' fanfiction could be how it explores the character's growth. It might show her dealing with a new and somewhat embarrassing experience in a human - like way, which could deepen her connection to Earth and its customs.
Another reason could be external threats that target Starfire specifically while Robin is trying to protect her but fails in some way. For example, a powerful villain might know of Starfire's weaknesses and use them against her, and Robin's attempts to counter the villain's attacks might not be enough in time, thus she gets hurt.
You can start by looking on popular fanfiction websites like FanFiction.net. There are often dedicated sections for different fandoms, and you should be able to find a good selection of Robin and Starfire stories there, including ones with the pregnancy theme.
Often, these fanfictions explore the emotional side of things. Nightwing might be protective and Starfire could be excited yet a bit nervous. The story could also include how they decorate the nursery and plan for their future as a family, all while still being superheroes.