Yep! It's called a Meet The Baby party! Sounds great! Have fun!
Actually it is not called a "Meet the Baby Party"...although the guests do get to meet the baby. I've hosted 2 showers after delivery. That is when the mom's wanted them. They were called "Baby Showers". I did everything just as I would for a shower before the baby was born.
Baby Shower = gifts are mandatory
Meet the Baby Party = gifts are not mandatory (or expected)
BTW...I've had 2 "meet the baby parties" for my own #2 and #3. I just combined them with our annual BBQ. Worked out great since they were born just before summer.