Hoyateach -- No preemies here, but there are two rambunctious boys about 8 next door who were born at about the same gestational age as your daughter, and I love seeing them playing baseball, football, basketball, whatever in the yard next door, and constantly laughing. So, good luck.
Have some experience with traveling and serious medical conditions though. My son had 5 long hospitalizations in 6 months in 2004, when he was diagnosed with leukemia. We took turns spending 24/7 with him at the hospital, when he was inpatient for those many weeks. But as the full-time worker in the family, I also needed to make money, particularly with his older sister just starting at Princeton. So, we had to make tough decisions sometimes.
Once, he got sick when I was away at a conference (just in DC three hour drive from Philly), and had to be hospitalized on an emergency basis. I generate a lot of clients at these conferences. By the time my wife and I spoke, she said she had things in hand, and he was out of any immediate danger. (She's a pediatric nurse.) I stayed at the conference for another day, and then came home.
Good luck with everything, both your daughter, who I hope grows up to be a wonderful person, and with the job interview. Hopefully, you can get some assistance from good friends for that day or two.