This might complicate your life a bit but as long as you have strong justifications as to why you are quitting your job, you should be fine.
You might be asked questions like:
1) Why did you change your job when you knew you would be attending grad school next year?
2) Was there something lacking in your job?
3) Weren't you confident of getting a good
MBA admission?
4) What do you plan to achieve during this one year in the new company that you haven't achieved in your previous company?
Also, please note that some schools ask for one compulsory recommendation from your current supervisor. So, I don't know whether you can start asking for a recommendation as soon as you enter your new company.

Even if you would and the person gives you one, since he hasn't known you for long, the admission committee may not feel good about it. I mean, what can a person say about you when he has known you for say 2-3 weeks (or months)? The minimum would be at least 5-6 months to understand a person!