FirstQuattro

Hello,
I just got my '02 A4 1.8Q a new battery a month ago. This morning while I was idling waiting for someone, the engine shut off suddenly, the battery light came on and the radio and AC were still on. I had to wait a few minutes and tried a few times to get it started again. Later when I was waiting at red light, the RPM went low suddenly like it's going to shut off again. I put some gas on and fortunately this time it didn't shut off.
My question: what could cause this problem other than the battery? could it be the alternator? I'm bringing my car back to the shop that replaced my battery tomorrow.

Thanks for your help!