I can't talk about the pierced ears, but as a Catholic, I know that baptism is *really* important to us
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It has to take place in a Church unless there's a life-or-death crisis (as in, the baby is dying imminently), so she can't call a priest and have it done at home. Basically, that's because baptism seals the child as one of God's children in community with the rest of His believers, so it's important that it take place in the community (i.e., in Church).
It could be a great way, if the situation is one that this is a good idea, of getting closer to the birthmom. You can and should be involved! While, as a non-Catholic, you can't be a godmother, you can be there for the baptism, help out, and shouldn't segregate yourself from it!! I'd encourage you to be there. It would mean a lot for birthmom and baby, and if you end up adopting baby, it would mean a lot later in life that you shared this important milestone.
Catholic baptism, other than a few prayers, is exactly the same as any other Trinitarian (Baptist, Lutheran, etc) baptism. It's recognized as valid by those other denominations, I believe (at least, we recognize theirs as valid, so I would assume vice-versa).