Will my baby remember me if I have to be away on business for a week?
We know that babies indeed form lasting memories beginning even before they're born! Many studies have shown that babies definitely know all kinds of things they have learned in the womb, such as Mom's and Dad's voices, and even the sounds of older siblings and pets. But they aren't memories in the way that we adults think of memories. Instead, the kind of memory at work in babies has more to do with associating good feelings inside their bodies (warmth, comfort, being dry and not hungry, etc.) with circumstances that surround them.
These early memories don't fade away with time, especially if they are reinforced with some regularity. So be assured that one week away from your baby will not erase you from her memory. That said, she may give you the cold shoulder for a bit when you return; try not to take it personally if that happens. Because the portion of our brain that processes the concept of time is not yet functioning in babies, they live in a kind of timeless state. Every moment is like an eternity. This is wonderful when things are going well, and a bit horrible when things aren't so good.
That's why it would be good for you to talk with your baby, and tell her what's what. Tell her you have to go away for a while and why. Just be honest. And keep in mind that babies know the innermost goings-on between their parents. Being as your baby thinks of her mother, in the early months, more like an extension of herself than a separate person, she will rely upon her mother's response to your absence. If you and your she are in agreement that the trip is needed and your partner is supportive of you taking the trip, that will help tremendously.
Finally, if you find that your baby gives you the freeze-out when you return, do what wise and clever fathers do when they wish to get closer to their child: Treat her mother with extra love and affection!