When I schedule young baby shoots, I now tell the parents to pick an approximate hour of baby happiness, and then to call me beforehand to let me know if baby schedule (feeding, sleeping) is going to plan. That makes life easier for everyone - I don't sit around doing nothing, and the parents don't fret that their photo session hour is ticking away unproductively.
I deemed the best lighting to be in the back yard. A hazy day, the light was lovely and filtered. However, the baby was very squinty outside, and though his giggled and laughed, he did so with eyes closed. So, we moved inside to the hallway, where there was a skylight - the second best lighting. Threw a big sheepskin rug on the floor (really large rug could've covered a small horse... I didn't know sheep came that big... maybe it was fake) and slid a hand knit cap (from Etsy.com, apparently) on the baby's head and lay him on the rug. He was impressively tolerant of the hat; many babies aren't fond of hats at all and do everything they can to remove them. But grown-ups like babies in hats so often there's a mini-battle.