Would I be able to get a DNA test on my child without my partner knowing?

If it is really important to you then you should get the DNA test, you all have a right to know the truth especially your son, it wouldn't be fair for him to always ume he is his father to later find he's not. You can do DNA tests through hair which should be easy to get hold of through clothes. You should really discuss the reasons for you wanting one and make him a part of it rather than doing it behind his back, have you thought about what you'd do if he's not the father how you'd break it to him if at all? I would make him see that you are doing it for your son as well as yourself so you can put the resentment behind you and accept the truth. It's what's best for everyone. Good luck and i hope the results come out he is the father.