K.S.
Congratulations! Send out the announcement and celebrate that baby as soon as you can!
I would add an "insert" to the envelope as a PS..."New Baby - New House - A Whole New World" so that A.) people wanting to send gifts (and who won't want to give a gift to the newest family member?) will know to wait and to use the new address (or to send it asap) and B.) people might take that as a good hint to delay a visit until the chaos of all these changes has settled down a bit.