Stuck in gender roles!!

I think this is about more than just being stuck in a gender role. If anything and I hate to say this, it sounds to me like your husband is using that old-fashioned convention to get out of helping you with anything at all. And the fact that he has not worked for so very long is very disturbing!! Is he committed to this marriage or not? Did he not promise to love, honor, and protect you? Or did he say some different type of marriage vows that I don't know about? If he promised to love you, he would NEVER stoop as low as to use gender stereotypes to get out of helping you raise your child or any other stereotypical female task. If he promised to love you, he would NEVER let you fix the sink, get the oil changed, fill the tires up or pull out power tools more often than he does.
May I ask, exactly what it is that he actually DOES? It doesn't seem like he's doing much of anything if you have to be pulling out power tools when he hasn't even had regular employment for 6 out of 8 months! I would be VERY worried about his committment to you, your child and your marriage if I were you.
I don't want to scare you but it sounds like things have progressed to a point where perhaps a little scaring is just what you need to realise that you are being given a "6" for a "9", and are not being loved by your husband. Whatever else he may be to you, he is not loving you the way a husband should love a wife.
If I had a husband and he did that to me, I would raise hell! That's just me though. And call me crazy but I actually wouldn't mind doing the stereotypical "female" tasks if my husband was the ultimate provider and did all the stereotypical "male" tasks. But I do draw the line with kids because I believe it takes two parents to properly raise a child, there is no stereotype when it comes to child-rearing.
How to stop it? It will not be easy, since it sounds like you have a serious problem. Have you tried to talk to him? Have to delegated tasks to him to get him to help out more? Communication is important. Maybe he just needs to be reminded what love really is.
I think you should perhaps suggest marriage counseling (for both of you) if you cannot convince him on your own that he needs to do more for his family - which includes you. I hope it turns out for the best. Be blessed!