A few things come to mind. First, it's never a bad idea to clean the throttle body. There are several walkthroughs available on this forum. Second, without knowing the maintenance history, it would be a good idea to install new spark plugs, air filter, fuel filter, and change all fluids. If you have maintenance records that are accurate you may be able to skip some of that. The spark plugs in these are supposed to be changed at 100k miles and should only be replaced with AC-Delco 41-103 plugs. Do not gap them. If you buy genuine plugs, they are already gapped. This basic maintenance will help improve overall driving performance and gas mileage.
As for the sudden jump in RPM - what you're describing is very subjective (slow pace, maybe pedal halfway down). It may be that at the point the RPM jumps the transmission is downshifting a gear if the RPM jump is over 700 RPM. If it's around 700 RPM, it may be the torque converter clutch unlocking. Either way, this is by design.
Another thing to keep in mind is that these vehicles are "drive by wire" - meaning there is no cable that runs from the gas pedal to the throttle body. It's all electronically controlled and electro-mechanically actuated. The computer manages ~everything~ in that engine/transmission. The throttle position is used as an input and computer makes calculations based on current RPM, current throttle plate position, current engine load, current gear, etc... and decides what to do with that throttle position input. With a stock tune, the computer is very conservative and errs on the side of providing a balance between torque and fuel economy, opening the throttle plate slowly until there's a good match between the throttle position input and the engine RPM. A good PCM tune can improve its behavior dramatically (opening the throttle plate faster, changing shift points, increasing fuel amounts, etc...).
Much of this is subjective, but cleaning your throttle body and checking maintenance records is essentially free. You'll need throttle body cleaner and some rags and a toothbrush to clean your throttle body. Fluid changes don't have to be crazy expensive. Personally, I'd start with the throttle body, air filter, and fuel filter. Depending on how it runs afterward, maybe spark plugs.