I left a top grad scheme after a week with nothing lined up because I knew it wasn't for me. Now that may sound crazy to some people and it probably was, but it was absolutely the right decision for me. I moved half way across the country for this job, before I arrived I was supposed to receive a job description, I never had one because my manager was on long term sick. So when I got there the job was totally different to what I expected. I spent a few days shadowing various people and I just knew that a job where I was basically stuck at a desk all day on a computer was going to make me unhappy. I also realised that I wasn't really "cut throat" enough for the job, I didn't feel comfortable with the way the people I was shadowing were treating other members of staff and how patients were just viewed in terms of money. The grad scheme was two years long and the thought of doing this for the next two years filled me with dread.
So after a week I told my manager that I'm incredibly sorry, but I've realised that I'm not the right person for the job and that I'd be wasting their time by sticking it out only to quit further down the line. I moved back home and started job hunting and got a few interviews, then the place where I did my placement year found out I was job hunting and phoned me up to offer me a job. I've been there since October now and I'm much much happier. I haven't included the grad scheme on my CV and luckily there was only a gap of a few months between me graduating and starting my current job, so it doesn't cause any problems.
I don't know your personal situation in regards to being able to financially cope without working for a few months, or whether you have a lot of work experience prior to this. If this is your only real work experience then I would strongly recommend sticking it out for a bit longer and looking for other jobs, you can explain on your application that you are leaving because of a lack of training opportunities. One of my friends did that 4 months into a new job and she still got interviews. If you have a lot of work experience prior to this job and it's making you that unhappy then it wouldn't be the worse thing in the world for you to quit, go home and look for another job. I did that and things worked out for me, it's not worth making your self that unhappy over a job.