I wanted to know more about how dogs work in CE, but found out that no guide existed, so here's a guide with all the info I've gathered so far, most of this info is shamelessly stolen from the wiki here Wiki - dogs, but the following section does have new stuff I've been looking into myself.

Stats

The dogs of CE have different tiers, as seen in the table below, but even within those tiers there's quite a range of stats. 

These ranges come from the base stats seen at the pet shop, and from people's dogs base stats.

Attack directly impacts the damage done to an opponent and is NOT affected by your opponent's armour. If your dog's attack is 50 it'll should typically do between 30-70 damage to your opponent.

Training

You can increase your dog's stats by up to 20% by maxing out experience and loyalty (+10% for each).

Loyalty can be trained by training or feeding your dog, which can be done once each day. This will reset to 0% if the dog is traded.

Experience is gained by fighting people, and stays if the dog is traded. 

I would recommend feeding your dog for loyalty and not training it, since training costs 25e while feeding it only costs dog food which can be bought for £6,250 at the pet shop.

Traits

Dogs can currently have one of these 5 traits:

• Growl - 20% chance of suppressing the enemy dog's ability to attack or use their trait for 3 turns
• Healing Lick - Increases the player's current life by up to 5% of Maximum Life
• Maiming - Reduces one of the opponent's 4 Battle Stats by 5% for the duration of the attack
• Metal Detection - Dogs will find small amounts of Cash during offensive attacks
• Tactical Reload - 20% chance of reloading a Weapon when this Trait triggers during offensive and defensive attacks

However, don't worry about a dog's trait when you buy it, since the trait can be changed by using Black Market Treats which can be bought at the pet shop for £62,500.

The general chance of a trait activating is equal to that dog's loyalty, so a dog with 20% loyalty would have 20% chance to heal you, but with Tactical reload it would only have 4% chance to reload a weapon given how the trait works.

How to get dogs

Each day, 3 dogs will be for sale at Victor's Pet Shop, if you just want to finish the starter mission of getting a dog, just buy a common dog to clear the mission, otherwise I'd aim for a rare dog for a good starting dog, since they're not rare enough that you have to wait for them for too many days, but rare enough that they can have alright stats. Of course at the end game you would probably want to have a good range legendary dog, so for that reason just keep checking in daily.

Dog House

In the pet shop you can also see a dog house, once you've studied the appropriate courses under animal handling in university, you'll be able to upgrade the dog house to allow yourself to own multiple dogs.

I am still quite new to the game and haven't unlocked these upgrades, so I don't quite know how they work, but since you can only use 1 dog for attacks, I only see this being useful for the sake of training extra dogs, either better dogs who haven't reached their full potential yet, or good dogs you want to sell to other people once you've trained up their experience.

awesome dude!!!