I am a SAHM with a three year old girl.
Your husband sounds clingy, alright. His insecurity is preventing you from feeling like a separate human being rather than a conjoined twin. I don't blame you for feeling smothered- If I were in your position I might be smothering him with a pillow in his sleep (kidding!)
Just because this wasn't an earth-shattering problem a few years ago doesn't mean you're not entitled to be upset now. Problems like these get exponentially worse over time.
Getting a job is #1 on my to do list.
I wanted to say that I completely understand how you feel, but I also feel that this could be a fixable problem. My husband was rather clingy when I got him, and it grew to get on my nerves. But with marital therapy he understood how his behavior affected me and he hasn't behaved that way in a couple of decades. If you think you could get him to go to counseling, I think it would be worthwhile, especially since you have a child. This in no way means that I think you should not get a job or find another way to empower yourself. I am just saying that I don't think this means it has to be a lost cause.
I think it's very difficult for some women who have worked and been financially independent and probably in charge of other people at work to be a SAHM.
If you've talked to him, and it doesn't sink in, then the next step would be marriage counseling.
Getting a job sounds like a good idea, but it's NOT going to solve the problem that you have with HIM.