I love my dogs too, I still refer to my first one as the "first born" as he has been with me for far longer than my son, but when I split from my ex, compared to DS, he was the least of my worries, I knew he would tag alone wherever I went, and as long as he had his food and blanket, he would be just fine, as yours will be.
Having said that, before I had children I took a lot of decisions with the welfare of the dogs in mind (including staying at home more than I should), so please do not do the same mistake as I did.
You cannot be held to ransom because he is depressed, but the fact that you are worried about him makes me think that you still care about him and perhaps, rather than a split, what you need is a serious heart to heart on how you are going to work TOGETHER (he also has to do his bit) to ensure the relationship survives his illness. Relate can be great at providing an environment where you both can talk about how you both feel and get to an agreement on how to move on, whether it is about saving the marriage or leaving each other.
The fact that he doesn't even want to hear about how you feel would certainly have me wishing to leave him wallowing on his self pity to take care of my own needs (not that I could do that easily, though).
IMO there are 2 ways people approach depression:
-Those that recognise the illness, take steps to fight it, understand the issues that may have caused it, and change things in order to be able to move on. Those are the ones who, once they are out of depression, look back and perceive themselves as "survivors", and..
-Those who, on being told they are depressed, get in a downward spiral where they claim nothing can be done, identify the issues that may have caused the depression but instead of doing something about them, spend all the time passing the blame and not taking responsibility of their own actions or lack of. Problem with these is, that by passing the blame they disempower themselves completely, as the solution to their problems is no longer something they can deal with or sort themselves with a little bit of help from counseling and ADs, but something that another person (and the rest of the world) has to solve/sort/change for them in order to move on.
I would say that if your DH is in the first group that it may be worth it to stick around, but... if he is in the second... you can talk to him about how he takes more responsibility or leave him to it, because remember, your life and happiness are as important as his.