By far the most comfortable sleeping pads I've used are Nemo pads. They come in different widths and lengths, so you can get ones that fit the space best. I think it's about 40 inches between the wheel wells (in a 4th gen) and a bit less than 6 feet long.
So two of these would fit and be incredibly comfortable:
NEMO Cosmo Insulated 20R Sleeping Pad with Foot Pump | NEMO
There are similar products available for much less, but in my opinion Nemo pads are more comfortable than most mattresses. The design of the baffles and the way they stretch makes a big difference in comfort.
You could get a double wide sleeping pad so there's no gap in the middle, and it would be less bulky than a regular air mattress. It looks like Nemo only sells a 50 inch wide one. That might work and it would just wrap around the wheel wells a little. Or some people have supposedly cut these things down and resealed them with an iron to change the size or shape. That obviously voids the warranty, and I wouldn't want to risk it unless the pad was really cheap since it might not work at all.
You could put pillows (inflatable or regular) in the unpadded space in front of or behind the wheel wells to make space for the dog without too much of a gap between the pillow and the sleeping pad.
You'll want warm sleeping bags, such as the Kelty Cosmic Down 20, if it gets cold where you're camping. The truck is not insulated at all. There are also double wide down quilts meant for backpacking that you might prefer for two people, but they are typically more expensive since they are less common. You could unzip some sleeping bags to be almost flat or even zip two together. Not sure how well that works with the Kelty bags. I think it works better with rectangular bags.
If you're tall you can unbolt the bottom cushions of the second row to gain some length. There will be a hole there that you could fill with something, or just put your feet there.
You can rig up a clothes line or elastic cargo net mesh between the hooks on the ceiling in the trunk (if the 5th gen still has these, I think it does). That's good for storing small items out of the way while you sleep.
You'll want some way to get ventilation. Just leaving the windows open slightly is not ideal because rain and bugs can come in. Even though the rear window on my 4th gen is under the spoiler it drips a lot if it rains heavily. Side window deflectors solve the rain problem, but not really the bug problem. I personally don't like them, though. One of these days I plan to make a panel that's the same thickness and shape as the glass around three edges, and has a groove for the glass to fit in on the bottom. I could close it into the window to hold it and seal it. Then the panel could have a small awning to keep rain out, over a mesh screen, and maybe even a small fan if I want more airflow.
You should also think about where you'll store the rest of your stuff while you're sleeping. You could move everything to the front seats, use a roof box or hitch mounted cargo box, put stuff under the truck, or even set up a tent to hold your gear while you sleep out of the wind in the truck.
