Looking for company that has school and will allow dogs...Too much to ask?

I just decided, after much soul searching that I do want to get my CDL and get out on the road. I live a little north of Seattle.
I am trying to find a company that I can get my training through who will also allow my little Scottie dog to travel with me. I realize
that it would not be possible for him to be with me during training. I am speaking of afterwards.

I know some companies allow pets of course if you are the owner operator but that's not the track I want to be on right now.
I need to find a company that will allow company drivers to have their small pet.

Today I talked to Watkins Shepard. They allow pets but no longer have their own school.
I really like the people at Central Refrigerated but they do not allow pets.
ANY help would be greatly appreciated. I cannot give up my best friend for this career change.

 

Well, guys, I mentioned in my post that I know it's not possible for him to be with me during training and I said I was speaking of afterwards.

 

I totally understand that there are people who are of the opinion that they need not be on the road. But for me, it's not an option. I am smart enough to not allow my dog to interfere with my safety and security. I know that I don't know everything at this point and I am sure there are aspects of the job that I don't understand. But I am a responsible pet owner. My Scottie dog is my world and he is very well trained. I don't really want to argue the points for or against, with all due respect to you guys, I just want to know who will allow pets because this one will be going with me on the road, no matter what. I am not leaving my man behind.

But I do have a question that relates to 1badaz28's response. How does a customer know if you have a dog in your truck? From what I've seen they just want their freight. Why would they even be in or near the cab of your truck?

 

But Flatbed...many truckers have dogs. MANY truckers have dogs. So...what percentage of companies you deliver to will do a search? 1 in 20? 1 in 80? 1 in 5?
I hear your advice and I appreciate all of the comments from you seasoned vets, but this hard headed girl is madly in love with this dog and leaving him is absolutely out of the question. It just will not happen. I don't want to be dishonest and lie to my company and take him anyway like many do. I want to do it the right way and be upfront and honest.