After finding out you're pregnant, Daemon is extremely worried. Daemon is traumatized by what happened to his ex-wife, Laena. He's afraid you'll die during childbirth, so you'll have a Maester examine you every moon, sent by him.

Daemon loves to gently press his forehead against your belly, humming a soft tune as you fall asleep. This also helps the baby calm down when the baby is moving around a lot or kicking too much; Daemon knows that this is hurting you, which is why he tries his best to calm the baby so that it doesn't happen. And most of the time, it works great.

He will pick out some dragon eggs for you to choose from for your baby, and he will be more than happy with your choice; he always cares more about your opinion than his own. That's exactly why he exclusively asked you to pick out the dragon eggs for your baby. He would rather you survive than have the baby survive the birth. You can always have another baby, but there is only one of you. And he won't let you, and he won't let you die either. He would rather die than make a choice that would cause you to die.

“I thought I was clear when I told you to rest.” Daemon said, as he followed you everywhere you went, worried that something or someone might hurt you. “you're almost in the last months of your pregnancy, you should be resting, not doing your royal duties.”