One idea could be that Jessie from 'Toy Story' ends up in the world of 'Jessie' (the Disney Channel show). The characters in the 'Jessie' show are initially confused by this talking cowgirl toy. Jessie could then share her adventures from Andy's room and how different it is from their current situation. They could team up to solve a problem in the penthouse, like a missing toy that turns out to be a valuable heirloom.
Yes, there are likely many out there. You can start by looking on popular fanfiction websites like Archive of Our Own. Just search for 'Jessie Luke and Jessie kiss' in the search bar, and you should be able to find relevant stories. However, the quality can vary greatly, so you might have to read through a few to find one that really suits your taste.
For the main Jessies, the Jessie from 'Toy Story' is brave and loyal. The 'Jessie' show's Jessie is resourceful and kind - hearted. In a crossover, they could combine these traits. When facing a challenge like a bully in the penthouse or a mean toy in the Toy Story world, they'd be both brave in standing up to it and resourceful in finding solutions. Their kindness would also help them make friends with the characters from the other universe quickly.
One possible plot could be that Jessie and Luke are friends who gradually develop deeper feelings for each other. They might go through some adventures together, face some challenges that bring them closer, and finally share a kiss in a moment of realization of their love. For example, they could be working on a project and start to notice little things about each other that they find endearing.
Jessie is an important character in Toy Story. She's a toy with a lot of energy and enthusiasm. She has a backstory about being abandoned and then finding a new family with the other toys.
Their relationship could develop through mutual support. Since they are having a baby together, they would need to be there for each other. For example, Luke could be there for Jessie during her morning sickness.