Arrival 11h55 Rotterdam Airport / Departure 13h40 Schiphol Airport with EasyJet

It did sound a bit crazy at first, but with a bit of luck, it should be doable, at least if you do have a driver on hand and your incoming flight is not delayed. Rotterdam airport is tiny, no time lost walking to the baggage claim area and exit or anything, you can literally be in front of the terminal building in 5 min.

At Schiphol, EasyJet flights depart from the H pier (departure 3/4, EasyJet check-in/baggage drop-off and the entrance to the pier are at the end of the departure hall). IIRC, there are signs outside and your driver should know where that is, it's the end of the last terminal. And you don't need to be at the gate an hour in advance. In fact, passengers have to wait in the H-pier lounge and the actual gate is only shown something like 30 min before departure time.

Taxis/professional drivers (but not regular folks, I think) can drop you on the upper level (departure), right in front of EasyJet's check-in desks and the entrance to the H-pier is right behind them (private cars can do it too, but a bit further away from the terminal building, see comment). The distances are actually very short compared to most low-cost piers and you can walk to the gate in 5-10 min. The main bottleneck is the security check, usually it's OK but I missed a flight once because of it (and EasyJet in particular won't accept any responsibility for it, they charged me €50 to change my ticket to the next flight).

Another concern is the motorway, I think you need more than 40 min at the best of times (especially if you obey the speed limits, which taxis usually do in the Netherlands, at least on the motorway) and delays are extremely frequent, there are traffic jams every day and more than one hour delay is easily possible on a busy rush hour. On the other hand, Monday is a bank holiday and 12 is not a bad time. Have cash on hand, taxis don't always accept credit cards in my experience.

For anyone who's going to try this in the future: I'd highly recommend taking a taxi to the Rotterdam Central station and then from there a train to Schiphol. The trains in Schiphol drop you off right in the center of the airport.

The big plus here is the train from Rotterdam Centraal to Schiphol. You have two choices - the Intercity Direct (25 minutes, it's a high speed train, specifically for that route, that makes no stops in between) and the Thalys (21 minutes, also high-speed, no stops in between.) The Intercity Direct costs €2.40 plus the normal train fare, the Thalys costs considerably more.

It's about 9 minutes by taxi from Rotterdam airport to Rotterdam Centraal, so that plus a 21 minute train means you can (in theory) get from airport to airport in 30 minutes.

The reason I prefer a taxi+train is that it gives you more options. If there's train delays (which you can check on your phone) then you're already in a taxi. If there's traffic, you have a train booked.