K.Z.
Here is a list I found of various ex-pat groups in Kuwait:
http://www.transitionsabroad.com/listings/living/living_a...
I suggest going to some of the foreign women's clubs where you will other foreigners and Kuwaitiis as well. They usually have coffee mornings and talks at least monthly as well as other events.
I know it is hard with a baby, but if you can take a class for fun like Arabic or aerobics or yoga, that is a good way to meet people.
Also, if you become a "regular" at a coffee place/tea place close to your house you will start to see the same people and get brave enough to talk to them. It is nice to have at least one destination each day so you aren't trapped inside your house.
I just moved to Seoul and am having to go through this as well.
As a side note, I lived in Cairo and taking Arabic was the best thing I ever did. Not only did I meet people, but you feel so much better once you can read. It takes a lot of discipline to teach yourself to read, so it is better to do a class or hire a tutor. I had several friends who were married to Egyptians and they had to take a class rather than learn from their husbands because it was too easy just to let their husbands handle everything and they weren't learning as much of the language as they wanted to know. It only takes a few weeks of a class to get enough to make your world much easier. You won't be able to read the newspaper, but you will be able to read street signs and simple things encountered in everyday life.
Now I need to work on learning to read and speak Korean!
Hang in there, you will have friends soon, inshallah!