Things I needed on long car trips with a baby, as well as international flights.
First, diapers. A diaper per hour in your carry-on luggage if you fly, including the estimated time in the airport. I never used cloth diapers but would think that even if you normally do, disposables are more convenient in a trip. If you drive, take a large pack with you and don't worry about shopping in a new place. Same brands are sold at some places abroad, but it's hard to know ahead if your particular brand is available. I traveled to Russia and Israel. In both countries Huggies which I preferred are sold, but in Russia they cost twice more and in Israel they are apparently made in a local plant and made my daughter uncomfortable. Of course it doesn't make any sense to stack diapers for several month. Change of clothes: two pair of pants in your carry-on, extra layer on top, small fleece blanket.
Second, you need something to carry your baby. If you already use baby sling, you will have it around all the time. It will double as a light blanket or a barrier between your baby and hotel linen. Some people use lightweight strollers, or umbrella strollers. I used a backpack than my babies were too big to carry them all the time in a sling. With a backpack, your baby is not underfoot, but on the adult's face level; your hands are free and there is no risk of run-away. Strollers won't let you go on interesting nature trails. Strollers are too cumbersome for the museums and in some not even allowed; strollers don't work on stairs. Even in the US not everywhere is wheelchair/stroller accessible, and don't expect it abroad. And a backpack weighs less.
Third, the portable crib or some baby travel bed. Most motels and hotels in the US, as well as in Israel, will provide the crib. I found this cribs great fun for older kids (they turn it upside-down and play shelter). Some babies will be uncomfortable in the new crib, and I know people who travel wit their own portable cribs for this reason. My babies felt most comfortable next to me anyway. I think portable crib makes more sense as a playpen if you are going to spend days at some places, like staying with friends.
I usually take about week's supply of clothes, even if I plan to travel longer. Laundering is usually easier than packing month worth of small things.
Baby food: well, maybe... Maybe a couple of jars or a bag of Cheerios for the airplane. When I traveled to Russia with my 11-month old daughter, she already ate some solid foods, but I was still nursing her. For two weeks of our travel she almost reverted to breast-feeding, and it felt most safe and convenient for both of us. She returned to her normal ever-changing emerging toddler food habits once we were back. When we traveled to Israel six month later, she was just weaned and ate mushed potatoes and local yogurt happily. By the way, in most countries other than US tap water is not considered suitable for drinking. I drunk it myself but gave babies bottled. In short term germs are more of a concern than non-organic hazards, so plain boiling may be enough if you don't know what brand of bottles to trust.
Medicine: children's acetaminophen (Tylenol) of ibuprofen (Advil) in syrup. Children's (or babies') apply to dosage. You can use adult-strength solution if you trust yourself with calculations and pouring half-teaspoons: the active ingredient is the same. Acetaminophen is milder. It also helps to tell simple viral infection from something more serious: if it doesn't lower the fever, call the doctor. Hope you will not need it. Some allergy relief: I pack it, superstitiously, every time. Never used, but who knows... Bandages -- maybe not with the baby but definitely with the toddler. Triple antibiotic cream.
See also: children, southwest kids.