Good video -- thanks for including it!
Now that you know how to reproduce the noise, the next step to determining the problem, is finding out exactly where it's coming from;
Run your engine with the Hood
up and either open the throttle manually from within engine bay, or have a friend press the accelerator pedal (obviously while in park) and listen to where the vibration noise coming form.
Have you taken a look at your alternator/pulley belts? Whats it look like? Torn, worn or very thin?
If it makes that same noise between those RPMs no matter what gear you're in, it could be your timing chain. Is your Check Engine Light triggered? If yes, by using an OBDII reader; what codes is it throwing?
How long has your Celica been exhibiting this noise?
In addition, (an inexpensive part but costly for the labor charges) would be if you notice your engine also "jumping" when you accelerate. That could be your rubber motor mounts. If they have gone "flat" or hard or are cracked, that could begin causing issues to start happening, such as this noise. If your engine is vibrating and there is no way to dissipate that vibration through the mounts, the stress gets shared with everything else connected to your engine. These are made of rubber, but some people replace them with aftermarket versions made of urethane.
As a side / very random question: Is that noise definitely coming from your engine? or could it be that your exhaust hanger has torn and it's dangling as your engine reaches highe revs -- such as a License Plate Frame
could do when some people blast their deep bass music.