Don't let them know upfront. Sounds harsh I know. The relationship is barely starting. Let them take some of the responsiblity also. I would tell people about my depression when they noticed that I was down.
I'm more inclined to agree with lightbeam, but this is a really good question to ask. I believe that some things are important to discuss before beginning a new relationship, but others can wait until the relationship has developed a bit.
It sounds like you're asking whether or not you should disclose this information to a new romantic prospect while you are
currently experiencing/entering a depressive episode--to which I would say--this isn't the best time to be pursuing a new relationship. I think that seeking out a new partner and building a romantic relationship is best done during a time in your life when you are emotionally stable, and preferably when you have stable social/emotional support networks around you. Then, disclosure of any serious mental health condition that you suffer from is, in my experience, typically discussed after the relationship has had time to grow, and probably within the context of experiencing the effects of that condition.
Both my ex and I have some troubling mental health conditions (major depression for me, bipolar disorder and a bunch of other things for him), and we didn't feel comfortable admitting this to one another until our relationship had grown (I believe we were 3-4 months in). The timeline for our disclosure to one another just happened naturally and in concert with experiencing our respective symptoms. In retrospect, I can't imagine full disclosure of these issues from the beginning being a good idea. I'm pretty sure telling someone you've just started dating about how suicidal you are could send them running for the hills, and who could blame them. Let some closeness build first.