Jennifer,
First of all, I'm so very sorry for the loss of your mother. I know first hand what it feels like to lose a parent, having lost my father 20 years ago. Many thoughts and prayers for you and your family during this difficult time. Treasure the memories you hold so very dear of your mother. They will help you through the most lonesome of days.
And please also accept my sympathies on the loss of your precious Katie. As others here have also gone through this pain, I too know the pain of losing a precious, beloved pet. I lost my Katie (aptly named from Scarlett O'Hara from Gone With The Wind) a few years ago. She was my first "baby" and was truly loved and spoiled by our family. I remember crying in the vet's office when she died that I had lost my baby. I had grown so attached to her, my world revolved around that little 5 pound fur-baby (as well as my 2 precious human boys). My husband wanted to get me a new puppy right away but I refused. My thoughts were similar to yours in that I didn't want to replace Katie. But I think my biggest reason for not wanting another dog is I just didn't want to allow myself to get that close to another fur baby. After a few weeks, I decided I was ready to think about another Yorkie and began my "hunt" for the perfect one. Through into this our looking for a house and trying to pack and all, it took me a year to find Gabby, or her to find me

We have had Gabby in our lives for the past 8 1/2 years and love her so much. She hasn't taken the place of my Katie but has earned her own space in my heart (one look and she had it!!). Now we've added Gage, our one year old rescue Yorkie, into the mix and my heart is overflowing with happiness.
I guess I could have taken the "short version route" and simply said you will know in your heart when it's time for you to find your fur baby. Katie can never be replaced, you know that and your family knows that. But there is room in your heart for another one....let it be your guide. God bless you and watch over you and yours during your time of grieving and healing. Keep us posted.
Suzi