vk1, please realize that I am only an amateur astrologer (as is bill), and the doctor's advice is what should be followed.
Generally in terms of scheduling a medical procedure, we want to look at the moon-- if it has made its last major aspect with another planet before changing sign, it is called "void of the course" which indicates she's less active and helpful. Also, Mars historically represents surgeons (and by extention, physicians) so we would like to see Mars well positioned. The main concern is the health of the baby and the mother, so it would be good to see no major hard aspects in your horoscope that could be avoided. Some planets' transits take so long that we're all pretty much stuck with them. Others, like the sun, moon, Mercury, and Venus, move pretty fast and may give us more leeway.
The timing with medical procedures is always hard to work with, however, because you can show up at the hospital at your appointed time, only to have to wait before it gets started.
"If it were me," I would go for February 1 or 2nd, if a weekend date is possible, otherwise Jan. 31. The reason I say this is that Mars looks to be in the best shape on these dates, and if you wait a bit, your little prince (or princess) will have a moon in a water sign (Pisces) which seems most compatible with yours and your husband's. Venus will turn direct on February 1, which will probably be an easier energy for your little charmer to handle than Venus retrograde. If we wait longer, no harm done but the child's moon in Aries may be a feistier energy for his/her parents to handle.
I don't suppose the doctor wants to work on the weekend! But if she has given you some options, then you can choose what feels best to you.
There is almost always some sort of difficult this-or-that transit going on in the skies, so a "designer baby" or birth is seldom possible, and no doubt your baby will choose just the right moment!
Bill, I think we can and should get beyond sun-sign and moon phase astrology as there are so many more factors in natal horoscopes and event charts.