Hi.. a 4wd camper is great to reach the more remote far north spots and camps
(
parkstay.dbca.wa.gov.au/search-availability/information/). RAC breakdown etc recommended (yes they are in Exm) and not sure what model it is but car parts are not so simple to find up here..
At this precise moment exmouth is at its peak in temperature ..and February will probably be warmer... on saying that the west side can be 15degrees cooler !
Avoid the school holidays like the plague that will be respectfully 'their' time .(not these ones..too hot

)..
If you are after diving and whalesharks also then march is better for the north
Bear in mind it's cyclone season now also but you can normally see them coming after formation ten days in advance....and know if they may effect you 3/4 days in advance ..
The marine life rejuvenates alot in jan and Feb as there are not so many people and the nice sharks come in closer and the snorkelling is better as they are not so scared off by so many people..
As for Esperance personally I would vote for Esperance in march.
It's really dependant on if you are chasing the whaleshark thing. They make a #veeeery# big deal of it in exm and a massive industry takes off at the end of February involving spotter planes etc buses and boats with runners going out earlier seeing if they can find them to 'kick it all off'.then they hype it up I got a bit bored seeing so many and moved on to other things

If you want decent time as a couple without so many packs and groups now is the time .i've met some lovely couples lately and am pretty happy for them that they are making the most of what I consider ningaloos most beautiful time.. the time it gets to 'recover' ..and yes allthough it can be gusty whatever you are doing foiling/windsurfing etc five days of the week you can be out there
Please note at this time of year working is cut down for everyone so be financially prepared as a can of chick peas is nearly double...not surprising because of the transportation required etc etc...
Also they have mass promoted the April eclipse so for sure things will be more difficult then..and prior to that(march)....

..even though there was a pretty similar one in Cairns several years ago and it didn't get so smashed
There are also stations you can stay at if you search around (and get on the water&snorkle at) that are not governed by the newish booking system above which is done with an honesty box and 'koha' (donation) as it was done before mass promotion
Goodluck