Check out that PIC-Multi-Calc file. That should tell you if 4Mhz will get you the 1khz you desire.
Also keep in mind that there's a 'granularity' with everything in the digital world. I haven't run the numbers, but, just for instance, with a 4Mhz crystal, you might get .975khz and 1.025khz with just a single number change, simply because you can't divide by a fraction. Same reason you can't get EXACTLY 9600 baud from a 20Mhz crystal in a PIC. You'll get close, really close, but not EXACTLY.
Bump up Fosc and you might be able to get the numbers you want...
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