How early can you fly with a baby? Context below

My Dad has liver failure and is not doing well at all. It’s really bad. I’m 38+4 pregnant. This is his first grandchild. I’m wanting to fly home to see him and my family but obviously cannot right now, so we are trying to figure out when to go. My question is, how soon is it safe to fly with a newborn- I’m worried about her getting sick due to airports etc. And/or, should the worst happen, and he doesn’t make it— god I hope he makes it... has anyone ever flown without their child soon after childbirth? I feel like this is impossible to even think of doing but should something happen, I have to be there. But my daughter. I just feel so torn.