The 25-year-old said she set up Sophie Bears on the anniversary of Sophie's second birthday, in July 2014.
"For support and comfort, when I lost Sophie it was really nice to know other people were thinking about me and who had been through the same thing.
"So in memory of Sophie, I want to let others know there are others thinking about them."
Ms Rogers wants to make the donation of bears an annual event and has set up a Givealittle page for other to help support her.
Each year she had got together the funds herself but was hoping to fundraise each year for the idea, she said.
The tag which comes with the Sophie Bear reads:
"To the family of an angel baby, I am sent to give you comfort and support in the days, weeks and months ahead as you begin this journey with empty arms. Please hold me close and know you and your angel are not alone. My mission is to be exactly what you need me to be. I come from a family who understand the grief of losing a child and I am sent with love."