If you consider you rocket a stiff body, than at all times all points on and in it will experience exactly the same acceleration. Therefore there is no difference between the two clocks that might be the source of the difference of the rates of these clocks.

There is no time dilatation here due to equivalence principle saying that acceleration is equivalent to acceleration, since both clocks experience exactly the same acceleration. [Gravitational time dilatation] [1] results from [the difference in accelerations due to the difference in gravitational potentials] [2] between clocks' locations. The distance separation between the two clocks in the spaceship does not entail any difference in accelerations due to different distance to the "center of acceleration". They can be treated just like two clocks distance-separated on Earth but located at exactly the same altitude, and therefore experiencing exactly the same gravitational acceleration $g$ (which differs depending on altitude). **Therefore the rates of the clocks will be exactly the same**.

[1]: http://en.wikipedia.org/wiki/Gravitational_time_dilation
[2]: http://en.wikipedia.org/wiki/Gravitational_potential