Well, as someone who has suffered from depression related to infertility on and off for about five years (and is now on Lexapro - a Godsend - and I've moved to adoption - yay), I would tell you, don't ask, just do. Stop over during the day - bring over a prepared lunch and have a real heart-to-heart conversation with her like you would a good friend. Ask her how she's doing. Ask if everything's alright. Ask if she's seen a counselor or doctor - especially if she's postpartum - hormones wreak havoc on women, but it's even worse if you're predisposed to depression.
Is she married? If so, you might want to ask her if she's shared this with her husband. If not, ask her if she has any family nearby or friends - if she has much support. (As a single woman I can tell you I sure wish people were more sensitive to how hard it is sometimes running a house, wishing I had a great husband to share my ups and downs with) Give her your number and e-mail and don't wait for her to call you or e-mail you. That night e-mail her to tell her how great it was to spend some time with her. Call her in a few days just to say hi and that you're thinking of her.
Don't just say, well if there's anything I can do - often when someone's depressed they HATE asking for help - you'll never get the call. Instead, say, go over there with a can-do, take-charge encouraging attitude "well, let's see, what can we do that will give you a lift? What is something that's really bugging you or getting you down?" Make a list of a few things you can do together. Maybe she's looking around her house and she's overwhelmed - maybe with an extra helping hand she can get her place organized. I'm single and I love when anyone offers to help me - two people can get so much more done so quickly.
Find out what it is that she's depressed about - is it marital, financial, or just feeling overwhelmed. If it's something you can help with, great, if it's not, maybe you can make some suggestions about finding a good therapist, a financial advisor. Maybe she can hire a teen for two hours each weekend to give her a mommy break - or to help with chores around the house.
Anyway, you are SO kind to think of her. We've really lost a sense of community in the last couple of decades, with people moving all over and keeping to themselves. It's great when neighbors show concern for one another.
At my peak, I was so depressed and my neighbor came over and asked me if I wanted to go see that Mel Gibson movie about Christ - I looked at her as if she was crazy. The last thing someone who is depressed wants to see is some deep heavy movie! LOL She's a very nice woman and I'm sure she meant well, but man, was she off.
