Traveling with a 4 month old

My husband and I are trying to plan a trip to New Orleans when our daughter will be 4 months old (it's for his brother's birthday, we're not going to go party or anything). We live in Central Illinois. What's the best bet: flying, driving, or train? She's a pretty "easy" baby so far- she doesn't fuss or cry much, but I'm worried she might on a plane. Has anyone taken a long trip like that with an infant this young? Any advice?