My brother has a daughter from a failed relationship. He gave up custody to her without a fight. My niece is 15 years old. I decided to look up her mother on FB and found her. I sent niece's mom a message just simply saying that I wanted to know how they were, specifically my niece.
I feel awkwardly nervous.
Re: Good idea or bad...
In that case, no worries! It's nice of you to extend the open arms. She may be wondering about her birth father and his family... never know.
I think it's great, you care and want to reach out.