Just to clarify the prerequisites, you also need to hold the JNCIA-Junos in addition to the JNCIS-ENT to become certified as JNCIP-ENT. And of course the JNCIS-ENT requires you hold the JNCIA-Junos.
The systems will let you take the tests in any order, but you will not receive the certification until all the prerequisites are fulfilled. So once all three tests have been passed then your JNCIP-ENT will become active.
I'm not sure what this will do to your expiration date. But I assume your three year clock will start with the JNCIP exam date but your certification will not be active until you pass the last of the three exams. so you will get a shorter term as a result as well.
The exams do get harder as they go up and they do not overlap question levels so it really does make the most sense to take them in order.