Long story short, yes and no.
Yes: you will need custom engine mounts and most likely a custom ECU/BCM, assuming the entire powertrain even physically fits. It's not just the engine, you'll need the transmission too as it is unlikely that the Toyota transmission currently in the Highlander could be mated to a Nissan engine. And since the transmission is connected to the driveshafts and the driveshafts are connected to the front suspension, you will need ALL OF THAT from the Nissan. Most likely, there will be some surgery involved to get different part to physically fit in the engine bay under the hood and just get attached. Just the custom engine mounts will cost more than a used engine for the Highlander.
No: swapping engines is a semi-common thing, but most people swap another engine that was actually available in this specific car somewhere in the world. That way, you know that everything will fit and that all the bits and parts you would need exist and can be had from somewhere. In your case, the 2003 Highlander had 3 different engines: a 2.4L inline-4, a 3.0L V6 and a 3.3L V6. You didn't mention which one you had, but you could swap for any of these 3.
Your best bet, if you want to keep the Highlander rolling, is to find a used engine from the junkyard. You are probably looking at $500-$800 just for the engine. Like I said, you could get any of the 3 engines that were available in the Highlander. If you get the exact one you currently have, you will only need the engine. If you get one of the other 2, you will need to get the engine with the engine mounts and all the accessories (it's called a "long block"), the ECU/BCM, and possibly the transmission.