Yes, it could be that the reason why she is constipated is because she is not getting enough water. Since she is eating, maybe you could feed her with canned food for a while. Canned food has quite a bit of water in it. You mention that she is on a special prescription diet, but not if it is dry or canned. If it is canned, that might be part of the reason why she is not drinking much, but if the subQ fluid soaked in really fast, then that does sound like she is dehydrated.