I'm not sure where to specifically find pregnant Hedwig fanfiction. You could try searching on fanfiction - dedicated websites like Archive of Our Own. There might be some creative works there that involve this concept, but it really depends on the creativity of the individual fanfiction writers.
One possible storyline could be that Hedwig has some sort of magical encounter that results in her being pregnant. For example, she might come across a magical object or spell that affects her in this way. Then the story could revolve around how Harry Potter and his friends deal with this unexpected situation, trying to find a way to take care of Hedwig and her soon - to - be - born owlets.
Hedwig can be characterized as a bit of a mischief - maker. Instead of just being a typical owl that delivers letters, she could play little pranks on Harry and his friends, like hiding their quills in hard - to - reach places.
Often, Hedwig develops a stronger bond with Harry in fanfiction. She might become more protective of him, going beyond just being his messenger. For instance, she could sense danger approaching Harry before he does and take actions to keep him safe. This shows her growth from a simple owl to a more complex character with emotions and instincts. Also, in some stories, she may develop relationships with other characters in the wizarding world, like the other owls or even some of Harry's friends, which further shapes her character.
In most of the original 'Harry Potter' series, Hedwig is an owl, not a phoenix. However, in fanfiction, the rules can be bent. Some fanfic writers might choose to make Hedwig a phoenix for creative and unique storytelling. It could add a new dimension to the story, perhaps giving Hedwig more magical abilities like the phoenix's ability to be reborn.
One common theme is loyalty. Since Hedwig is Harry's owl, the fanfictions often explore how deeply loyal she is to him and vice versa. For example, in many stories, Hedwig will go to great lengths to protect Harry or deliver his messages no matter what the danger.
There is also 'Harry, Lily, and Hedwig's Adventures'. This one takes the trio on a journey through different magical realms. It's a more action - packed fanfiction where Harry discovers new things about his mother through their adventures together with Hedwig. The author does a great job of creating vivid descriptions of the magical places they visit and how Lily's presence affects Harry's growth as a wizard.
I'm not sure of a specific fanfiction titled exactly that, but a lot of fanfics in the Harry Potter universe might have a scenario where Hermione looks after Hedwig. You could search on platforms like Archive of Our Own. Just type in 'Hermione and Hedwig summer' and you'll likely find some interesting reads that could potentially be what you're looking for.
Because their relationship in the original series is so pure and deep. Hedwig is Harry's constant companion, and fanfiction writers like to explore that bond further, adding more emotional depth and different storylines.
The mental link between Harry and Hedwig in fanfiction can often be a tool for the author to create unique plotlines. Maybe Harry can communicate with Hedwig telepathically, sharing his thoughts and feelings, which Hedwig can then use to help him in some way, like warning him of danger when she's out on a flight.