A powerful demon might be the main antagonist. The demon senses the pure and strong magic within the baby and wants to corrupt it. Natsu and Lucy would need to use all their skills and the help of their friends to fend off the demon. This would also test their relationship as they're responsible for the safety of the baby.
Perhaps an organization that believes the baby is a threat to their plans. They might think the baby's existence could disrupt the balance of magic in some way, so they send their agents to capture or eliminate the baby. Natsu and Lucy would then have to fight these agents to protect the baby. They'd face various challenges and dangerous foes within this organization.
It could be a dark wizard who wants to use the baby's power for his own evil deeds. Maybe the baby has some special magic that the wizard thinks can help him take over the magical world.
It could be a new, powerful dark wizard who has a grudge against Fairy Tail. This wizard might manipulate Natsu into kidnapping Lucy to create chaos within the guild. The dark wizard could be after some powerful magic that only Lucy can access, and by kidnapping her, they hope to force her to give it up.
It could be another dark mage who sees the potential in baby Natsu and wants to use him for evil purposes. This mage might view Zeref as an obstacle in getting to Natsu.
Maybe a rival guild that is jealous of Fairy Tail's new addition. They might think that having a baby with such strong magical potential in Fairy Tail gives them an unfair advantage. So they try to kidnap the baby to either keep it for themselves or use it to bargain with Fairy Tail.
The main antagonist could be a powerful and ancient fairy who has been banished long ago but now returns to seek revenge on the fairy world. And Lucy, being a new and important part of the fairy world, becomes a target. This antagonist might have unique and dark magic that makes it extremely difficult for Lucy to defeat. Also, the antagonist could have some sort of grudge against the fairy queen or king, and Lucy is caught in the middle of this power struggle.
Well, perhaps in this fanfiction, Natsu calling Lucy 'baby' is a sign of a new level of closeness in their relationship. It could start with Natsu protecting Lucy in a dangerous situation and instinctively calling her 'baby' as he holds her close. This then leads to Lucy being a bit flustered at first but gradually getting used to it and even liking it, and it becomes a special part of their bond.
One possible plot could be that Natsu and Lucy accidentally end up taking care of a baby dragon. They struggle at first with things like feeding it and getting it to sleep. But as time goes on, they grow attached and learn a lot about themselves and their relationship in the process.
Well, perhaps the story could start with Lucy finding out she's pregnant. Natsu is initially shocked but then becomes super excited. The pregnancy is filled with little adventures, like Natsu trying to build a perfect nursery using his magic in a rather clumsy way. And when the baby is born, it brings a new sense of hope and family to the whole guild. Everyone pitches in to take care of the baby, and it grows up surrounded by love and magic.
It could be another guild that sees Natsu as a threat. They might find out about Lucy kidnapping Natsu and try to use the situation to their advantage. For example, they could try to steal Natsu's magic or get information out of him while he's in a vulnerable state. Another possible antagonist could be a character who has a grudge against Lucy. They might try to stop her from getting away with the kidnapping or use it as a way to get revenge on her.
It could be a dark wizard who wants to use Natsu's connection to the Dragonoid for his own evil purposes. This wizard might have set the trap to either steal Natsu's power or to use him as a sacrifice to gain more power related to the Dragonoid.
It could be an old and powerful vampire lord who sees Natsu as a threat to his rule. Since Natsu is a new and different kind of vampire, the lord might want to eliminate him.