Given the description of the problem, I think the comments are exactly right, this is an issue with your transmission. Now you need to determine if it's just fluid level, or if there is something more serious going on.
Couple of things you can do, first, follow the instructions in the comment by @DucatiKiller. That will get you into the proper fill level. If the problem does not go away, pull out the transmission dip stick (please tell me you have one) and see if the fluid is a nice bright red. If it's getting dark or if it smells burnt, then you have a bigger problem internal to the transmission.
One other thing you can do, is look at the data from the OBD II port. If you have a scanner, many modern cars include the temperature of the transmission fluid as a data field from the OBD II port. You didn't mention what year your SUV is so I don't know if it will have it.
Another test is to move the gear shift level yourself. Does it shift right away? If it does, then maybe you have bad vacuum lines to your transmission. Basically there's two pieces to this, the transmission needs to know when to shift, and it needs to be able to shift. The vacuum lines are part of how it knows when to shift. If they are cracked, you can get what you are seeing. Sadly the pull might be saying that it's not vacuum lines, but the transmission internals. But, that's not 100%.
Things to look at:
- What year is your SUV?
- What are the results of getting the fluid level to be correct?
- What is the operating temperature of your transmission fluid as seen on your OBD II scanner?
(Btw, if you don't have a scanner, and do have a smart phone, you can buy a $15 or $20 Bluetooth dongle that plugs into your OBD II port and talks to a free app on your cell phone. No need to spend almost $100 on a scanner.)
I hope that helps!