Can I file my taxes separately or with my common law partner?

You are common law so you would file common law. You each do your own taxes as individuals but you have to put your spouse's information on your return because they use both of your incomes to calculate all the credits just like they do for the GST/HST and CTB/UCCB. CRA already knows that you're common law. You ARE common law and have been since your child was born. Make sure that you have your spouse's net income before you attempt to do your own return. A common mistake people make is not including that. Then the tax software automatically calculates your return based on your spouse having no income at all. Since they use both of your incomes to calculate the credits, it really screws them up. You may end up getting more than you would be entitled to but, since it was in error, CRA will ask for all of it back and then some.