If you have special medical needs try to get some extras stocked up. For a healthy baby there are still some consideration to think of here. You will be outdoors and exposed to the elements more, make sure you have lotion to put on any chapped and windblown skin. You will want to make sure you have baby Tylenol on hand to combat any fevers that might occur. You should also have a good baby thermometer to be able to check for the fever. Sometimes if you are cold it is hard to judge how hot baby actually is. You should also have some kind of Vaper Rub on hand. Baby will get snotty and snuffly and it is nice to be able to open up their airways and get them healthy faster. Another consideration is having baby Orajel on hand. Parents rely heavily upon little icey things to ease baby's teething pain but in a bug-out situation you will not have access to ice. The Orajel can bring some much needed relief to baby and the parents' ears.
Carrying Baby:
If baby is small enough, consider carrying baby in a front backpack. This allows you to still carry all of your gear on your back with baby in the front. Remember though baby is going to grow and you will not be able to use this front-pack long so make sure you have a good back carrying pack ready to go as well, just in case you are bugged out for a longer period of time.
If baby is too big for the front pack I recommend a Ergobaby pack. I have used this pack for my baby extensively. It is not bulky and it is very comfortable for a long period with a heavy child. My son is now three and weighs 45lbs and I hike six miles with him on my back no problem. It is like carrying him piggy back but he doesn't have to hold on. The only problem with this pack is it does not carry much else than baby. You can hook your sleeping bag and/or bivvy sac under where the child sits to carry a little extra gear. An additional pack that you could carry on your chest would be a great addition to this setup.
Feeding Baby:
Even if you are planning to breast feed baby long term, which would be ideal in a bug-out situation, pack as much formula as humanly possible. High stress situations can cause a woman's milk supply to dry up and you don't want to be left with a hungry baby and no milk. To maximize the amount of formula you can carry take it out of the bulky packaging and vacuum seal it into smaller serving sized baggies. That way it will last longer and you don't have to worry about carrying around an open pack of powder and losing half of it along the way. Have some extra bottles with different nipples styles. Some babies prefer different types of nipples. It is best to know what your baby likes before you are dependent upon them to feed your child. You also want to have lots of extras because if you are not sanitizing the nipples properly they will get moldy and will have to be disposed of. Make sure you rinse and care for them well.
Changing Baby:
You will need a supply of cloth diapers, safety pins and soft cotton clothes for wiping baby. You may want to carry some extra bleach so you can sanitize items better. Remember you must let bleach air dry after application for it to have its full effect. An alternative method is to hang the items in the sun. The sunlight destroys bacteria and should help to keep baby from getting an infection. Make sure you have lots of diaper rash cream on hand. Baby will get much worse diaper rash wearing cloth diapers. Plus, the rash cream works well on chaffing that will happen from the extensive walking the adults are doing.
Clothing Baby:
If you are bugging in you should have a supply of shoes and clothes to meet baby's needs as they grow. They grow fast so you will need to be prepared. Don't throw out your old clothes or take them to goodwill. Store them for the future. They can be re-purposed into clothes for baby and multiple other things.
In a bug-out situation you will want to carry the next size up if your space and weight allow. It would be nice to carry all the sizes you will need but you'll already have a lot more to carry, like a baby, so scavenging is going to be key in a long term situation. Remember that baby will get cold too. Make sure you have hats, gloves, scarf, and a very warm one piece suit. You can always take clothes off but you can't make them magically appear.
Baby Medications:
If you have special medical needs try to get some extras stocked up. For a healthy baby there are still some consideration to think of here. You will be outdoors and exposed to the elements more, make sure you have lotion to put on any chapped and windblown skin. You will want to make sure you have baby Tylenol on hand to combat any fevers that might occur. You should also have a good baby thermometer to be able to check for the fever. Sometimes if you are cold it is hard to judge how hot baby actually is. You should also have some kind of Vaper Rub on hand. Baby will get snotty and snuffly and it is nice to be able to open up their airways and get them healthy faster. Another consideration is having baby Orajel on hand. Parents rely heavily upon little icy things to ease baby's teething pain but in a bug-out situation you will not have access to ice. The Orajel can bring some much needed relief to baby and the parents' ears.
Touchy Subject:
I don't know how many of you have learned the history of the holocaust. I haven't studied it extensively but I have heard many stories of mothers who suffocated their babies in order to keep them quiet when they did not want to be found by an enemy. As a mother of two beautiful boys this concept absolutely horrifies me but I can understand the logic. Lose baby and keep yourself and the rest of the group alive or save baby and everyone gets caught and baby probably gets taken from you anyway. The answer to the problem: Learn to make chloroform and have some on hand. Consult a doctor now and learn the proper amount that you would need to use. I understand that baby is going to feel miserable after the encounter but if it is the ticket to keeping everyone, including baby, safe then I think a headache would be worth it.
Feel free to elaborate on my list and suggest anything I might have missed. Realize that both mom and dad will have to carry extra gear because baby won't be able to carry their own gear and whoever is carrying baby won't be able to carry as much of their own gear as well.