As professor Farnsworth would say it, "Good news, everyone; we are expecting a baby."
My problem is to find a place to leave the elder sibling during delivery. We moved to a new place, where we have no family/relatives, and are too new to the area to request help from a neighbour/friend. I am sure others have faced such situations, is there something that could be done in situations like this?
Update: Now that my daughter is born, thought I should update my question with what I actually did.
There were two services that were very helpful.
1. The website care.com allows one to register (monthly cost of ~35$) and search (quite comprehensive) for babysitting help. The site claims that all people listed are done so only after a thorough background check. It even allows one to broadcast a message to registered babysitters asking for last-minute help.
2. The second service is nannypoppins.com, which is sort of a website+call service. If you call their number when you immediately need help, they will find one from their registered on-call babysitters and help you.