With the laptop you should do very well. I have flown at least 20 flights with my now 21 month old alone. Never with a laptop. I am jealous.
Just have a good attitude. Make it fun and exciting for baby. Let her run around in the terminal. Try to get her to nap on the plane. Make sure you bring fave blankie/lovey. (duh)
With the head cold. uh... Be careful. A couple flights ago I had a minor sinus thing going on and on the way up I noticed i couldn't clear my ears. (I used to fly in the military, so I know all the tricks. And FWIW, we never ever were allowed to fly with a cold because of this.) No big deal. Until coming down. I had the most pearcing pain ever imaginable in my ears. One worse than the other. I thought for sure blood would start trickling down my ears. I was very close to getting the attendant.
Now, I survived. My right ear ended up clearing about 10 hours later. It was very painful, and for a couple days my ear wasn't right. But, now I am fine.
I don't know if this was a specific kind of cold or what, but after this experience I will thinkn twice about flying with a cold. I have heard of babies having issues with their ears when they fly. Mine naver has.
I don't want to scare you, but if your baby is turning red screaming on descent, that is what is probably going on, and God be with you.
Have fun on your trip!