Intermittent stumbling/shaking on acceleration from stop

Hi Everyone,

Just wondering if others have had this problem;

2010 with 166k miles.
Runs perfectly almost all the time but will occasionally be very rough and unbalanced on acceleration from a stop for a few seconds, then runs well after gaining speed.
No engine check light on.
Most noticeable in stop and go traffic.
Mechanic suggested it might be fuel pump but I am not handing over $900.00 unless necessary.
Car just completed 2,000k trip and climbed mountains no problem.
Could this be a transition problem as motor starts up? It seems to happen most often when the battery charge is low.

Thanks.

Sorry - should be in gen 3 forum.