It is pretty hard to earn recognitions without the age-level recognition book, especially at home.
Most councils have a council shop.
If not, you can order the book from the Girl Scouts of the USA National Equipment Service online. Sometimes, troops use their funds to purchase books for everyone, or girls who have moved up pass books down. By encouraging her to do her best and providing an environment where she feels she can succeed. Be a sounding board for ideas and actions, but let her make decisions and take action on her own. If she asks you to take a role in the project, you may do so, but under her direction.