Speaking as a parent, you may get away with it for a few months, but as your child grows older you will need full time childcare if you want to work full time hours. You would be better off to continue working (I'm assuming you are working at the moment) and do your exams before considering working from home. Being in paid employment is usefull for things like paid holidays, paid sick leave etc. It's also quite easy (if expensive) to get an infant/toddler looked after, but it gets a lot more complicated when they start school.
Best of luck with child and work!!!