I did something very similar after I graduated from university with my Mechanical Engineering degree last June. Throughout my undergrad, I struggled with severe depression and anxiety, but it was never properly diagnosed because I was relatively high functioning on paper. I went travelling with a friend after graduation thinking that once I was out of the pressure cooker that was school, I would feel better. I was very wrong, but something clicked for me while I was gone and I realized that I was very suicidal and needed serious help.
When I got back, I moved back into my parent's home, I took time off to see a psychiatrist, got on medication, and tried to get better. That was in August. By October I mustered up enough energy to start applying for jobs again. I made an Excel spreadsheet with companies where I had contacts or where I had an interest in applying, and started churning out online applications/cover letters. I found that focusing my search was much more effective than what I did during my last year of university.
I only had one interview in November, but I really wanted a position at this company, and so I spent weeks preparing for the interview and doing research on the company. A friend of mine referred me for this job which was extremely helpful, as my resume probably would have been lost somewhere in the pile without a contact. Even in my depressed state, I knew this was something I really wanted and I was able to motivate myself to work for it. I ended up getting the job in January, and it doesn't start until April, which has given me a bit more time to recover. Although I'm currently unsuccessfully fiddling with medication right now, I hope that come April, I will be able to jump into my new position with a sense of purpose.
I think a few other people have said this, but at this point, it's fairly common for people to take some time off after graduation. In my interviews, I didn't mention anything about the mental health struggles, but I did say that I was exhausted from university and I wanted to give myself the time I needed to recover so that I could dive into my new job with vigor. I did also go travelling, which was another excuse. Additionally, many of my classmates who graduated with me in June did not find jobs until the end of the year or the beginning of 2015. It is a tough economy out there right now and I don't think there is anything wrong with saying that you had a temporary job while you were looking for more permanent, degree-related work.
I wish you luck with the job hunt - it's tough but you've already started clawed your way out from the spiral of depression, which is a feat in itself. If you have any questions, let me know. I hope my story can help you in some way!