Although you can not prevent acquiring Alpha 1-antitrypsin deficiency (since it is inherited) - there are some things you can do.
Some people with Alpha 1-Antitrypsin deficiency are very likely to develop lung disease, and others are merely more susceptible to it. In the case of being more susceptible, you are much more likely to acquire COPD and lung disease if you smoke. If you live a healthy life (excercise, and not smoking) you can actually increase your life expectancy. It makes even more sense for you to abstain than the general population.
There are treatments that can supplement your healthy lifestyle choices.
If you have a low enough level of Alpha 1-Antitrypsin in your blood, it can be possible to receive some via IV. This can add the protection to your lungs that your body is unable to provide.
Eventually you may get to a point when your lungs are unable to do the work they need to do anymore. In this case you may be eligible for a lung transplant.
More information about treatment and prevention can be found at:
Mayo Clinic: COPD and Alpha 1
