Question : What kind of jobs in the can I get in South Florida if I want to keep working and still raise my child on my own?

The ability to work in the US will depend on the type of visa you have. If you have been transferred by a company, this might not be a problem. However, if you are the trailing spouse, you have to find out if your visa allows you to work.

South Florida is a large region with very well developed industries and professional activities. There are positions in retail, schools, real state, tourism, entertainment, customer service, etc. On a professional level, many professions require a State license, i.e. physicians, psychologists, pharmacists, lawyers, architects, etc.
If you are legally able to work, most schools provide or have arrangements with after care opportunities.