This is so personal. The decision is truly yours, as it's an individual one. Some people are able to manage the delivery of a eulogy with aplomb; others can't even bear to think about doing so. Before making your decision, digest their request. Think through how you truly feel about it. Talk to your friend's family. Are others going to be speaking about her? Then go with your intuition. If you decide you want to do it, fine. Write your talk from your heart. Think of some light, special stories about your friend. Practice your talk. Have a shortened version ready in case you find yourself breaking down. Ask the clergy person who will be officiating at the service for any tips on preparing/delivering a eulogy.
If you're completely overwhelmed by the prospect, and feel that you must decline, it's OK to do so. Thank the family for offering the honour to you. Explain that you don't feel you can do it, and be honest as to why. They'll understand. Offer your help in other ways: if you partake in the service, you could read a Scripture passage. You could offer to help the family with plans for the service and for any reception afterwards (if there is one). Maybe you could take on the project of preparing and printing programs for the service.