There are four alpha hemoglobin genes. In alpha thalassemia, the most common condition is that one or more of the alpha genes is deleted, resulting in no alpha hemoglobin being produced by that gene. Silent carrier is one gene deletion. Alpha trait or minor is two genes deleted. At the most, alpha trait results in a mild anemia that can't be treated with iron. When three alpha hemoglobin genes are deleted, is called hemoglobin H disease and can range from mild symptoms to severe thalassemia, requiring regular blood transfusions. There is also the more severe Hemoglobin H-Constant Spring, which is also three gene deletion, and usually results in a lower Hb and transfusion dependency. Four gene deletion alpha means no alpha hemoglobin can be produced. This results in death of the fetus during pregnancy or a stillbirth. In some rare cases that have been diagnosed in utero, babies have survived by being transfused while still in the womb.
If your girlfriend has not been tested for alpha thal, she should before you have children. If you are alpha trait and not silent carrier and she was a silent carrier, it would be possible, although with low odds, that you could have a child with three gene deletion. Silent carrier is very difficult to detect so family history is very important in diagnosing. Alpha thal is much more common in certain ethnic groups and this is also used for diagnosis. Genetic counseling would be a very good idea. Even though, it may be very likely that the most your child could be is a thal minor (beta or alpha) it would help to know if there is any other unknown risk.
Your children could possibly carry one beta thal gene and/or one or two alpha thal genes. It is extremely important that all carriers be aware of their status as this information is vital when they decide to have children. If a beta minor has children with another beta minor there is a 25% chance of having a major. With alpha thal, the possibility of having children with three alpha thal genes should be avoided.
If your gf does not carry alpha thal genes, there is no reason to not have children as the worst case would be minor. Keep in mind that regardless of who either of you have children with, there is the chance that your children will be minors, so it should not be a factor in whether or not you marry her. The same risk of passing on your respective thal genes will be the same with any partner.