Answer

There are halakhic decisors who are lenient regarding the sterilization of a female (as with humans) and argue that it is a rabbinic prohibition. That is somewhat strange, because with animals there is no obligation of "be fruitful and multiply." But even so, it is still a prohibition. If you were doing this for your own needs, perhaps there would be room to be lenient (after all, sterilization is no worse than slaughter), although that too is a bit of an inference based on the reason for the verse. The same would apply in a case where the rabbit would in any case be unable to produce offspring (because there is no male accessible to her). In any event, here you are not doing it for your own needs but for the animal's needs. I think the reasons you gave are not sufficient to permit a prohibition. Fine—if the rabbit is already suffering and then this is done. But to violate a prohibition מראש because she may need it later does not seem to me to be a sufficient reason to permit a prohibition.