Tell us about yourself!
You might want to look at the BlindSight devices at jordycanid.com
Here is the link for the first one I found 4 years ago. Your is a fraction of the size. He actually used a back-up alarm package powered by AA's. It had a battery life of less than a day. Your's looks MUCH more practical! There is imaging SONAR available for dogs, but dogs with bad hearing can't use it. Yours would work for them if it vibrated or something like that. Don 't worry about 40khz. It is near the typical upper limit of canine hearing and most dogs are pretty insensitive to anything much above 35khz or so. If there is going to be a problem with 40khz it is that there is so much of it out there. If you can swap out for 75khz transducers that would eliminate that problem. FYI, I'm an engineer with some experience with both SONAR and RADAR.
Sorry! Here is the missing link! The big package on the side is full of AA's. I believe he mentioned that the dog has since passed, but I may be thinking of another one.
I have seen a number of very similar projects over the past 2-4 years (on Youtube, mostly). I think all were Arduino based, but used a much larger sensor array...car ba ckup stuff, I think! The thing they has in common was very short battery life. I know there are processors now that are much less power hungry. I also notice your sensor array is much smaller. What is the battery life like with an alkaline 9v?