There could be a chance, but perhaps it may be an idea to leave it a while?
I think that during the assessment the following areas would be explored:
You have suffered depression (not in itself a reason to be turned down) but are still on medication. I think they'd want to know whether enough time has passed for you to recover and rebuild your resilience. If you get another period of depression, what support do you have around you? Have you had or are you having counselling to work on any underlying issues?
In addition to this, that you are currently experiencing stress to the extent that you are looking to leave work. This could be no problem but I think they'd want to explore how resilient you are and how you will manage stress when fostering - it can be a really busy, tiring and stressful job.
Also, how long ago did you adopt your son? They would possibly want to know that he has had enough time to attach with you and settle into your family before adding in the complex dynamics of a foster child. And how would he manage having a baby who would take up your time and attention?
Whether the local authority needs carers for babies varies from area to area, but that would make it viable in terms of your accommodation.
That you will be on benefits is not a problem so long as you won't be in any way relying in any income from fostering. Carers can go for long periods without placements sometimes, therefore no payment.
That you have adopted and therefore have experience in integrating a child into your family, adapted to meet his needs etc. could be a real positive.
I'd give the local authority or some agencies a ring to discuss your interest with them. Maybe get their view on whether now would be the right time for you and your family.