While little Hailey definitely brought joy (and a little chaos) to the Potter-household, the Child of the Crawling Chaos' presence didn't however change the state of Magical Britain as a whole. And Magical Britain was in a state of turmoil. A civil war between Lord Voldemort and his followers, the Death Eaters, and Dumbledore's group of vigilantes known as The Order of the Phoenix with the ministry caught in between the two factions.
During the times where the Death Eaters were losing against the Order of the Phoenix, some of the more deranged members of the Death Eaters sought the assistance from the cosmic horrors from beyond the realm of humanity and received none. Though considering the fact that most of those cosmic horrors were entities that were either malevolent or apathetic towards humanity, the entities ignoring the Death Eaters attempted summonings was a good thing. The few who showed some form of benevolence towards humans were those who took an interest in the realm of humanity because they were bored. One of the most notable entities who had an interest in the realm of humanity out of boredom was the Outer Goddess known as Shub-Niggurath, the Black Goat of a Thousand Young. Though the fact that Shub-Niggurath was an Outer Goddess of fertility with multiple cults under different names, quite a pervert and (in a kind of twisted way) quite a fan of romances, it wasn't too incomprehensible why Shub-Niggurath had an interest in the realm of humanity. Shub-Niggurath was also one of the most caring out of the Outer Goddess, finding all life precious, even if her varying valuations between various species were all over the place.
In a rather weird (by human standards) show of familial love (having somehow managed to convince Nyarlahotep to let Shub-Niggurath be the godmother of his child) Shub-Niggurath sent her goddaughter a present for her first birthday, or rather a later birthday present that was sent and set up on her first. The present was a seed of some kind that would, if given the proper amount of care, grow into something really special in a few (Earth-)years. While it wasn't easy to tell, the seed wasn't from Earth. To be more specific, the seed came from somewhere else entirely, from a world beyond the stars of Earth's solar system, if not even further beyond that. Not that any of the Potters could actually read most of the note that Shub-Niggurath left with the seed. Hailey couldn't because she was too young (by both human and Outer God standards) to read while the child of the Crawling Chaos' parents couldn't really read the note due to rather illegible writing. Though considering that most Outer Gods usually didn't write notes in the first place, it made sense (and actually kind of impressive that Shub-Niggurath actually could write in English (albeit with very barely legible writing)).
Weird gifts from entities beyond human comprehension aside, the Potters couldn't help but smile as they watched little Hailey peacefully sleep in her bed, hugging her blocky bee-plushy while doing so. Even after a whole year of being Hailey's parents, they still found it difficult to comprehend how happy her presence made them. The fact that they couldn't have children of their own due to being on the receiving end of some curses from a magical shootout and that adoption was as close as they were gonna get to having children of their own probably helped though.