Dog Gate

I havent seen one yet. Just those with the back seats down. They arent for the Prius but sort of fit.

 

To answer your question, yes, it is possible.
I haven't found one specifically designed for the Prius yet. I guess the demand isn't high enough for a company to manufacture one. I've tried a few of the so called "universal" pet barriers and they don't fit well enough for me. (I have Corgi's and the gaps are large enough for them to squeeze through.) With larger dogs they might fit well enough to keep Fido from joining you in the front seats.
Petsmart sells a few different kinds of barriers, and they were understanding when I brought mine back for a refund. You could try them, Pet Co didn't have to many in stock but was willing to order them.
Foster and Smith (Drsfosterandsmith.com) has a few listed in their catalog. They sell a Net Style which might work well for small dogs, along with other types as well. They also have a fair amount of "Cargo Liners for the back hatch area.
You might want to look into what Thule and Yakima have to offer, although they look like what everyone else is selling.

 

We found that our German Shephard would fit perfectly in the back hatch area. We put in the cargo net and took out the mat - works great and she enjoys the view!

 

I have a "flat vertical grate" that I have used behind the rear seat. We also found dog harness - seat belts that connect to the rear D-rings. Our Aussies stay in the rear.

 

I just raise all of the headrests to their highest positions...keeps my small black lab in place.

Jack