You will not lose your US citizenship by becoming a permanent resident of Canada or a citizen.
- Supposedly now takes 12 months, but processing time depends on a number of factors
- The work permit process is much slower – you’ll need to work in Canada for a year before you apply for permanent residence through Canadian work experience (given that you are a doctor, you can immigrate right now)
- Immigrate as a skilled worker or self-employer professional – the former should take a little more than 6 months
- That is a question you need to do some research on.