Since I was Big/Lil Coordinator (Sister-Mother) for my chapter I can help with this

For initiation we give our little sisters silver lavalieres. They were only $8 from UniquelyGreek.com. You can make her a scrapbook, make her a candy basket/jar. I know some chapter that buy t-shirts and then put letters on them to give to their lils. I made mine a poster and put it on her door as a suprise that said Big Sis and Alpha Gam love (her name), and then made a pouch on it and filled it with her fave candy (Sour Gummi Worms) with pictures of her and her pledge class. You Could make her a friendship/sisterhood bracelet with your sorority colors. You can also buy her stuff and Uniquely Greek has really great inexpensive stuff.