What should I do if my baby is too young for a flu shot?

Shoot everyone else. Flu shots are recommended for anyone over 6 months of age. If your baby is younger that that, make sure everyone else in the household or has contact with your child gets the flu shot. Also for younger infants it is a good idea to avoid contact with anyone who has a cold if possible.
Baby carriers. P.S. We had good results with taking our 3 week old to disneyland by carrying him in the baby sling all the time when out of our hotel room. People tend to respect the parents' personal space better than they refrain from touching a baby's hands or face when they are exposed in a stroller. (be aware that some infant slings have been recalled -- positioning can close off the airway!).
Cocoon them. Cdc recommends a technique called "cocooning" to prevent disease in babies too young to vaccinate (or others unable to receive a vaccine, such as immunocompromised). This means having baby's caregivers receive the vaccine to provide a layer of protection around her/him. Other strategies are good handwashing, minimizing taking baby into crowds, and asking ill contacts to not visit or wear a mask.
Vaccinate caregivers. If your baby is too young (under 6 months) when flu shots are available, the next best thing is that all caregivers (parents, nannies, baby sitters) should get their flu shots to give the baby a ring of protection from the flu. You should also be careful taking your baby out and being around sick people. Continuing breastfeeding can also increase protection.
Immunize family... ...Members and caregivers in contact with the baby, and avoid unnecessary contacts. Also, of course, handwashing and proper hygiene, and breastfeeding, contribute to the baby's protection.
Handwashing. To prevent the spread of influenza and other viral infections, there are a few measures to follow: frequent handwashing, avoiding taking very young infants to crowded places such as malls (esp. Under 3 months old), and avoiding letting friends/visitors who are sick hold the baby. No family members should smoke since smoke exposure greatly increases the risk of respiratory infections in children.
You can get the shot. Children under 6 months cannot get the flu vaccine, but those around them can and should. This includes the parents, siblings and all other caregivers and close contacts. In addition, good hand washing and avoiding large crowds, daycare and sick individuals lessens the risk of catching the flu.
Immunize caretakers. Immunization of the parents and any caregivers and avoiding crowded places during flu season will help to reduce the risk of exposure for the baby. In addition, studies have shown that immunizing the mother during pregnancy can give protection to the baby.
Protect your baby. Make sure all household members are vaccinated as well as caregivers.
Vaccinate everyone. Vaccinate everyone around the baby, avoid exposure to sick people and lots of hand washing will help prevent the spread of the disease.

Related Questions

Do babies get antibodies in breast milk after mom gets a flu shot?

Yes. Whether these are really protective for the child is harder to prove. Breastfeeding is a personal decision looking at one's whole life situation. Best wishes. Read more...
Not enough. The antibodies in breast milk are predominantly IgA, otherwise called gut antibody, because they help prevent germs from attaching & invading the gut wall. Mothers make IgG after a flu shot, and a little comes across in BM but not enough to be considered protective. If the kid is 6 mo they can get a flu shot.Before then we encourage any of their contacts to get one to "cocoon" baby in protection. Read more...