I think you did a great job on the email, and obviously it shows since she seems genuinely happy for you!
I was very nervous about telling my girlfriends as well. The last two years have not been great for all us with some concurrent losses. So sharing the news was hard, but they were happy for me as well.
Coming from the infertile end, (10 years here and finally pregnant) I would much rather hear it from my friends/sisters/coworkers mouth or words (email, text, phone call etc) instead of hearing from a third party person. Nothing hurts worse the having a friend of a friend tell you "so and sos pregnant and she felt bad to tell you herself" we are really understanding I thought your email was very nice. And I'm pretty sure that your friend is happy to have heard it from you then through the grape vine!
Re: ***UPDATE***: Tell me I did the right thing - telling infertile friend about the baby. Long