If they operate like any big box store loss prevention/security, which I know that they do because I worked in loss prevention on multiple levels and in several large stores attached to malls, they wont tell anyone that the dog alerted on you, they will hang back and radio someone in their camera room to follow you around on their cameras while they wait for PD to arrive then they will join up with PD and have them confront you for them. Mall security and store LP agents don't do hands on security or confront anyone anymore unless absolutely necessary.
If the dog walks up to you from behind or you think it alerts on you, you probably won't be confronted, but your best bet, if your carrying, is to leave mall property if it does because you will be greeted by a police officer shortly after. Also, huge news flash but no mall or retail security agent has to physically follow you to your car to see your license plate or the car that you get into. I can personally attest to the fact that even the cameras at the, all but abandoned and outdated, Eastfield Mall can read plates and ID people across the street at McDonald's, and Chicopee Wal-Mart AP can watch people all the way across the shopping center at Home Depot and read plates and ID people over there and all the way out to Memorial Drive where they can see it. Some of the newer stores have 4k PTZ cameras with 20x optical zoom and digital zoom on top of it, and now lots of them also have the parking lot security trailers with extra cameras on masts that have people watching the parking lot full time. Even the stanley sliding doors at the entrances to most places get you on about 8 different camera views in the entrance vestibules on your way in & out. There is almost nowhere in any shopping mall you can't be seen and ID'd on camera at any given time.
I have personally had to deal with working in stores and on properties that have "no weapons" policies and have had to deal with people obviously carrying weapons that patrons of the store noticed and complained about or people obviously stealing or up to no good that had weapons, we never confronted them without police at our side, and often we would wait for them to go outside and the police would confront them outside on the sidewalk. Most people working in security are going to be pro gun or aspiring to be police officers, they aren't going to be worried about the average dude walking with his family that's concealed carrying that prints a bit, they are looking for ghetto goblins and bangers with extended mags poking out of their sweatpants and other stupid shit. Under no circumstances would we ever confront or attempt to stop a shoplifter or someone visibly carrying a weapon, we had to call PD and let them handle it, and that's including having the PD help us serve the person with a no-trespass notice.
If you want to steal from any big box store, openly carry a large straight knife while wearing a covid mask and get in and out before the PD can get there and your all set, leave the store on foot and get picked up out of sight and never come back. LP won't touch it with a ten foot pole because of the visible knife and the PD won't bother unless your making a career out of it or it's a huge dollar amount.