2003 Toyota Tundra fuel pressure

Im having a problem with my truck accelerating and idling. First - an example. This has been going on for about 3 weeks and mainly when the car is not quite warmed up yet. But it is not limited to that condition. When I come to a complete stop, then accelerate, I am able to accelerate for a second or 2, then it acts like I just took my foot off the gas for 1-2 seconds, then accelerates normally. Today was the worst condition I have felt. I was driving up a hill waiting in line to cross an intersection. When I let my foot off the brakes, I hit the gas. After I hit the gas, my truck hesitated and started rolling backward slightly. I then floored it to try to get back up and nothing happened. After about 4 seconds, it responded with quick acceleration. And this was a right after I cranked it, but the truck was still warm from driving earlier.

The idling problem exists mainly but is not limited to first cranking the vehicle and letting it idle. Also, I have noticed that when the air conditioner cuts on, it pulls the rpms down even more. Not enough to stall the truck, but lower than usual and my ac does not cool as well with this condition.

my first guess was that it had to be something in fuel. My plugs and wires are brand new and this vehicle is very well kept up. I have rented a fuel pressure tester from autozone (never been used).

my question is: is it right to assume that it could be my fuel pump or my fuel pressure regulator?

if so, how can I determine this using the fuel pressure tester, how do I use the fuel pressure tester for this application, and where do I connect the fuel pressure tester?

also, my check engine light is not on and has not turned on since I have been having this problem.

any other thoughts on what this could be?