Hi Nathaniel,
First, congratulations! Of our six children, four were adopted through foster care.
Three of them came as babies, one only fifteen days old, the other five months and the third eighteen months. The other child came into our care at age 10. Shortly after adopting them they were baptized. The oldest one was obviously not an infant, but she was baptized as part of the household. She was willing to be baptized and at least in word, is very compliant with our faith, though I don't believe she was (or still is at 14) ready for communicate membership. If she was actively opposed to the faith, that may have been a different story, but that was not the case.
Lastly, at least in Pennsylvania, it is illegal to baptize foster children. I think it is also prudent not to baptize them, since it is not guaranteed they are part of the (permanent) household. However, when that legal change occurred, we were excited for them to receive the sacrament.
Again, congratulations! I wish you the best in these adoptions. When my wife first approached me about fostering and adoption, I told her that I didn't think I could love "other people's children" the same as "my own." When the first child came into our care, he didn't feel like someone else's child. He felt like our own. In God's perfect plan, he wasn't able to stay and was adopted by relatives (wonderful Christian people!). I quickly realized that it is parenting, not genetics, that makes them "your own."
Blessings,
Tim