Would this be a sound case for me to be able to adopt the kids?

My girlfriend and I have been together for going on two years in January. When I have the finances to do so, we plan to get married (within the next 6 months). She has two children from a past relationship, but the guy whom she had the children with has not tried contacting her or the children in what will be 2 years on Christmas, and when he did it was not even for a 10 minute visit. Me and my girlfriend have had a child together, and have seriously considered and decided on me adopting her other two children as well. I am 21 years of age, currently unemployed (medical issues but getting them fixed) and a full time college student as well.