Hi Ross,
There is nothing wrong, you can apply your kid (from your singleness as what you said, lol) at the same time, for sure you dont want him/her to left alone there in PI, pitty, so you can include him to your application alright, and about your querries, if you allow to work ? Yes you can, your applying spouse visa is it? Just wondering, if you can work because who gonna look for your kids while your working ?