Being in graduate school while having a newborn was one of the hardest things I've ever done (oh yes, I was also working full time). I'm a very active father by neccessity (health issues with my wife). So, it's not like I could check out. I would hesitate recommending doing both based on my experience.
Depending on your age, waiting may prove more useful.
Male, Straight, Poly
“Instead of getting better and better at avoiding, learn to accept the present moment as if you had invited it. And work with it instead of against it. And making it your ally rather than your enemy.”