Yes to the microchip! We got Cody microchipped on his first vet visit at 13 weeks. Just to be clear, while a lot of folks choose to wait until their dog is under, that's not a requirement. It's about a 2 second procedure and it's not that big of a deal. Animals can be chipped at any time and any age (well, okay, don't know about those wee ones under 8 weeks... but that's it!). Which is convenient, because they can get lost at any time or any age as well.
Both of my cats (who never get out of the house) are chipped as well. If there's a way to take an extra precaution to keep your baby safe in emergencies, it's worth it. 100%.