Search for Toyota parts in Google and have your VIN number handy to get the correct part. You may not need it, but it is a good idea. There are numerous dealers with that part.
You can easily install it yourself if you have some tools and are able to aim it. I use my garage door or an open field to aim the lights so that they are on the road and not in the air. Since you are installing high beams, you just need to get them on the road and a couple of hundred feet down the highway. Alternatively, if you get them installed by the dealer or other mechanic, they should aim them for you. Personally, I would bring the car to my body shop and have them do it. They will get the right part and do a good job of installing it.
The name the Toyota parts department gave you is correct. There are other names for it also, such as "headlight assembly high beam". There is a left and right side part number.