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In short, yes, your engagement ring can be your wedding ring. There are pros and cons to having a wedding band in addition to the engagement ring.
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Not traditionally. It's called a wedding set for a reason--there are two rings in it. The engagement ring is the one with the stone or stones on it. The wedding band usually doesn't have a stone in it. They're often sold together; you give her the engagement ring when you propose, and the wedding band at the ceremony.
More tradition: she wears the engagement ring into the ceremony on her right hand. The left ring finger, where the whole set goes after you're married, will be bare until the groom places the wedding band on it during the "with this ring, I thee wed" part of the ceremony. This puts the wedding band closer to her heart.