I think a little overprotective.
Is your dog an unpredictable animal who has shown aggresive tendancies toward your daughter when she pulls its fur or bitten someone else or is this a complete and "total what if?" If your dog was any of those things, and you let the dog stay in the house in the first place, and your husband knows that there is a real danger, then I get it. I just don't see it otherwise, even if this was not the best idea, and there is a remote chance of something bad happening, it is not reason to fight with the person you share your life with.
Unless there are tons of other clear examples of him doing things that are a real and present danger to your child and not just what if- what if- what if- then what your husband heard you say is that he is an idiot and damnit, he should shape up and do things like you do. If my spouse talked to me this way, I might be spiteful and stubborn too. I would not be surprised if he had the very same impression about you, and do you really want to be in a stand off about your baby?
I just think you need to listen to what he thinks because if this is the best example of how "lax" he is, then the rest of your examples must be really small stuff. A remote "what if" with debatable probablity behind it does not say "absolutely no sense of safety" to me, and all my kids are still alive and well (one for 18 years now) so I think your husband deserved more consideration.
One thing is sure, if you let every little thing that you do differently than he does escalate into an argument you are never going to get him to see your "side" of anything. If he is spiteful and stubborn already, picking a fight over a difference of opinion is not going to help him be less so. I certainly hope that you eggagerated when you said that he does not have the ablity to be cautious, because if he lacks the ablity, why do you ask how to get him to be more safety conscious? You just said that he lacks the ablity! That says to me that you need to step back just a little and look at his "side" because your "side" has some questionable logic behind it, and if your husband is anything like mine, he has already pointed this out to you. Try to put it in a way that even an "idiot" (who has his feelings hurt and is mad at his wife) can follow.
Drop the "sides" and parent together, he has just as much to say about this baby as you do. If you applogize to him first, then you just might be able to sit down and discuss this as equals. He disagrees with you, and adults do not demand that other people who disagree with them admit that they are mistaken or change their ways. My experience is that human beings respond very poorly to ultimatums anyway. Maybe he is in the wrong, but you went wrong by pointing it out to him like you did.
Unless you left out something like not using car seats, smoking in the house, leavng her in a hot car to get a six pack in the stop and go, passing out drunk while she was awake on the sofa, giving her peanuts, hotdogs, or grapes to eat...you know, there are so many really dangerous things that he could do that have no debate about them what so ever.
M.