I have known quite a few people who have worked from home as medical transcriptionists. Here are a few tips I can give you. Since you will be listening to doctor dictation, you need to work in a quiet room- so while the baby is sleeping or preoccupied with something else. Since your baby is so little, that shouldn't be a problem. I knew of a single mom who worked early in the morning and when her daughter woke up, she would work while she watched Sesame Street and then they would have the rest of the day together. Most of the medical transcriptionists I know say that the work isn't very challenging but the benefit of being able to work from home is what they like the best and it isn't a difficult job.
Employers will test your skills before they will even look at your resume so you need to get good training. You are going to need to learn how to spell medical terms, how to recognize them when you hear them, how to set up a medical record, and a really good course will help you increase your typing speed. Most medical transcriptionists are paid by production- per line or report. So the faster you can type, the more amount of money you can make in a smaller amount of time. I found a great resource for what types of subjects a good medical transcription course should include at http://bestmedicaltranscriptiontraining.com/choosing.html
If you are unsure about all this, you can see an online demo of a medical transcription course. That way you can see what it would be like training for this career. The demo is at http://www.careerstep.com/demo/?uid=ref10077
As far as pay, according to the US Deptartment of Labor, "Wage-and-salary medical transcriptionists had median hourly wages of $15.41 in May 2008. The middle 50 percent earned between $13.02 and $18.55." But again, they usually get paid by production so the faster you can type, the more money you can make per hour.
I could go on and on so I hope this is what you are looking for. Good luck!!!