Is it worth continuing with graduate school if I can't obtain an assistantship?

With only a year to completion, I would try to stick it out and switch to a PhD if you are the main source of income for your household. If you are the main caretaker of the child, I think you should take a break and finish it up later when your child requires less of your time. It will also give you a chance to think about what direction you are truly interested in going.

almost all grad programs offer assistantships that pay a monthly stipend as well as your tuition expenses. such programs are called "funded". one of the rare exceptions is the mba program. it is not normal for mba students to be funded. you might wish to change to a phd program. all phd students in just about every business school are funded. you will be required to do some work. either teach one undergrad course or be a research assistant for one of your professors. the latter is the better choice if you are doing a phd because the research assistantship can seamlessly lead to your dissertation.