You don't have to give her anything. Some chapters have their pledge classes make things, like pillows, as a group to give to their Bigs so you might want to ask your New Member Educator that question.
If you want to give your big something than that is up to you. I showered gifts on my little (even though we're technically not supposed to) and she gave me lots of stuff in return. I didn't expect it, but it was a nice to get them.
So, it really depends on what you feel.
Introduce yourself on our Roll Call and I hope you stick around and post!!