I think it's a wonderful idea to try to get young kids involved in Ramadan, even if they're too young for fasting. Try slanting the focus of Ramadan away from fasting and onto some concepts that are a little easier for kids to grasp.
Ramadan provides a great opportunity to reflect on one's character and foster a sense of community among family members -- even for little ones. So while a 4 year old may not be able to understand the full significance of Ramadan, she can surely learn something meaningful from it.
After doing a little research, I found an article that contains some helpful tips and suggestions for including young kids in Ramadan. The woman featured in the article takes her young children to homeless shelters and animal shelters to help them gain some perspective on important issues, such as respect for others.
Another easy (and fun!) way to get young children involved is by coming up with some crafts that have a Ramadan focus. The article suggests a couple of ideas, including a Ramadan calendar and creating your own prayer beads.
Our family is Muslim, and I shared your question with several other Muslim mothers as well. I didn't find consensus among these mothers with regard to children and fasting. Some felt that children under age 5 should not fast, others thought it was good to let them try to fast. I suggest talking to your child's pediatrician and your imam about this, to learn more about the physical health and spiritual aspects of this decision.
Personally, we have not yet required our daughter to fast. She is eight, and attending public school in the U.S. There is extensive scientific evidence proving the importance of nutrition to learning. It is also very hot right now, and easy for children to dehydrate during recess or lunch playtime. While we understand the significance of this very important observance for Muslims, we are not forcing our daughter to fast during school.
However, we do read the Qur'an and pray with her, and explain (and demonstrate) what Ramadan and being Muslim means. We also got a book from the library that you may also wish to share with your daughter, "My First Ramadan," by Karen Katz. We also encourage our daughter to volunteer to help others, and to be kind and respectful. We regularly remind her of how blessed we are, and how there are many people around the world who struggle to eat, gain access to clean drinking water, and survive extreme natural and societal conditions with few to no resources. So while she may not yet be participating in the fasting, she is definitely learning the values of Islam and the spirit of Ramadan.
Below are some additional resources on this topic. I hope this helps!