Congrats on your new little one! And welcome to MDC!! 
The copper IUD is a hormone free option that works really well for a lot of women. However, I am personally scared of them as they seem to cause a lot of strange side effects for some women and the mechanism for how they work is not even fully understood. I have to admit that having a piece of metal in my uterus doesn't really appeal to me either.
There are many barrier methods out there like condoms with spermicide that are pretty effective with proper and consistent use, contraceptive film, diaphragms, etc.
Lastly, I would recommend looking into charting to see if that might be the right option for you. Charting your cervical fluid and basal body temperature is such an empowering tool that allows you to see when you're fertile, when you ovulate, how long your luteal phase is, when to expect AF, if you're pregnant and if there is anything of concern happening with your cycle. It really takes the mystery out of it! If you're interested in starting to chart (to just get to know your cycle better, to avoid pregnancy, or later to achieve pregnancy) I highly recommend reading Taking Charge of Your Fertility. It's full of interesting information that I did not know about my body prior to reading it. You can log your charting data on a free site like www.fertilityfriend.com and share your charts with us so we can give you advice, tips, and help deciphering anything that's confusing. There is also a Charting to Avoid thread you can join to learn even more about the rules you need to follow to avoid pregnancy with charting. Warning: do not rely on charting to avoid pregnancy until you have charted for several months and understand the rules well. Use back up in the meantime!
Since you are only one month postpartum you don't need to worry about pregnancy yet. Statistically speaking you are very unlikely to ovulate prior to 56 days postpartum. After that knowing the signs of returning fertility will help you know when you need to start protecting against pregnancy. If you are breastfeeding you can follow the rules of LAM to protect against pregnancy for about the first 6 months. Here are some helpful links about that:
http://www.kellymom.com/bf/normal/fertility.html#prevent
http://en.wikipedia.org/wiki/Lactational_amenorrhea_method
Breastfeeding can make charting more difficult and there are extra precautions you would need to take while your cycles regulate postpartum and during the weaning process. If you are interested in more information, just post!
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