I'm very sorry for the loss of your baby.
While I think there is not neccesarily any massive medical reason why you should wait to start TTC again, I think there may be a few things that it might be worth considering before you start trying again in earnest. I've had four mc over the years at various stages in the first trimester, and these are just my thoughts based on some of my experiences.
I developed infections after two of my mc. These were very painful and had to be treated with antibiotics. The infection only showed up a few weeks after the mc and I think treating them would have beem medically and emotionally more difficult if there had been a possibility that I might have been pregnant. Infections need to be treated prompting to prevent potential difficulties with fertility.
Emotionally, you will probably find the next little while very difficult. It does get better, but the early days can be pretty grim. I'm now 6 months pregnant again, only two months after my 4th mc. I found the early days very, very difficult and I had a sense that I had got pregnant almost too quickly. I don't think I had got through the raw grieving bit before being thrust into the roller-coaster of post-mc pregnancy all over again. I'm not sure I would recommend this.
Also, from a purely practical perspective, if you mc at 12 weeks, it may take 4 to 6 weeks for hcg to leave your body. If you are actively trying to get pregnant this first month there are a couple of things that might be worth knowing. Ovulation predictor kits will not be reliable as they respond positively to hcg in your bloody. Therefore, a positive OPK does not guarantee that you are ovulating. Also, I would recommend testing with pregnancy tests regularly until you get a negative test. Otherwise, you run the risk of taking a test 4 weeks after your mc, getting a positive, thinking you are pregnant with a new pregnancy (when you are not, it it just a hang over from your old pregnancy) and then being devastated when your AF starts.
Best of luck with whatever you decide to do.