Doctors are so goofy sometimes. "Cannot" is a big sign that you need to see a new doctor. If he/she didn't explain why, in a way that you could argue with, then they don't have a logical leg to stand on.
Now, I am not a big fan of starting food that early ... but I am sure aware that it isn't a "cannot do it" situation. Pff.
I aimed for the 6-months-only-breastfeeding thing recommended by the Pediatricians now. But three of my four were interested in food before that, and I considered meeting their individual developmental needs more important than following medical "standards" that have nothing in particular to do with individual reality, change with the blowing social winds, and in our case, had already again and again proven to be fearmongering and inapplicable to our babies. The "standards" are very useful if they can be explained to you and if you can argue with them, because then they are adding information to your parenting, and the doctor would learn about your baby as an individual.
Standards are not useful if they are preached.
I had one that breastfed exclusively to like 10 months. I had two that started eating at 4 months (mashed up real food--I don't bother with rice cereal or any of that, but that's partly because I waited until the baby was developmentally prepared, by their signals and reactions, for food), and they both weaned themselves 'earlier' (both after a year). The fourth started eating at 5 months but still nursed (for comfort) almost to two.
If your baby can't handle your work schedule, can you drop those work times, just for a few months? Because it will probably only be a month or two before she starts sleeping longer and more soundly, in general. (We forget that every stage is pretty short, at this age. Not like when a kid is fourteen ;). )
--K