First I am so sorry for your loss, it does cut very deep and will be with you for a long time, sadly.
We had a duo that were inseparable, they were like twins. When our Lab Sofie passed our Pom Zachery was just so sad, it was hard to get him to eat or have any interest in anything.
After a couple of weeks my DH said enough, it broke his heart to watch Zack and his depression so he found a beautiful Lab puppy and brought her home.
Of course at this point Lucy was small so Zack took an interest in her and they slowly bonded but what it did was it gave Zack something to focus on and watching that puppy was a full time job.
On to four years later Zack died suddenly and in my whole life I have never seen a dog so inconsolable as Lucy was, it was so heart breaking for all of us but Lucy just stop living, had no interest in walks, swimming or chasing her chickky (tennis ball)
It took about a month we found the right dog to rescue...he was a throw back Pom I wanted to adopt.
Lucy was ok but looked at me with eyes that were still sad but that quickly changed when she found she could play with and rough house with this guy named Bubba.
To this day they are joined at the hip and all is well with their life.
Everyone has to decide for themselves what is right for them, for us it's always having two dogs and while it hurts so soon after a loss it has worked very well for us.
Sher