ARM9 defines the processor core (but even then there are variants; yours being ARM962EJ-S), but most on-chip peripherals and support hardware including clocks, PLLs, and interrupt controller are vendor specific, you you would have to port your hardware initialisation and device driver code, and make sure that you choose a device with a comparable peripherals set to the ones your current code uses.
Moreover if the code is written in C or C++ rather than assembler, much of it may be prtable to other architectures, particularly if the application layer and hardware abstraction layer are well defined.
Another issue may be whether your existing implementation relies on any particular OS or RTOS; you may need to select a device that supports the same OS in order to reduce the porting effort.
Finally, a non-programming point, but just to keep you out of trouble; you need to be sure that you own the rights to the code you intend to reuse, and that the original client has no claim on it.