The weekly pass does not entirely cover the journey from the airport into Vienna. You will need a supplement. The system for paying the supplement will change on July 6, moving from a zone system to a system based on distance.
As noted already, the weekly ticket on the Wienerlinien runs only from Monday-Monday. There might be better and cheaper ways. Regarding your kid, it depends on what time of year and the age of your child. If you can share your details on length of stay, where you are staying (general area), month of stay and age of your child, it will make answering your question a lot easier.
All that said, when you arrive at the airport, I always suggest taking a pre-paid taxi if you are 3 or more - it is worth it at 32 Euro. Then once you are in town, you can go to a ticketing machine and/or Wienerlinien desk and figure out what is best for your needs. Honestly, if you are staying in the center of town, you might not even need to use public transport.