Congratulations! Being asked to give a speech in honor of your niece on her Bat Mitvah is a great honor. Traditionally, the parent or relative talks about the importance of this spiritual milestone and highlights some key Jewish attributes that the child has developed. Since you aren't Jewish, you can focus on the moral and ethical attributes of your niece with examples of her compassion, caring, joy in learning--you get the idea. Below are a few links with some examples and explanations of the ceremony and various speeches. Once you have an idea of what you want to say, you can run it by your brother or even the rabbi to get feedback, but it's not likely that anything you say about your niece that is from the heart will insult anyone.
Best wishes! You'll have fun....
whttp://www.justwriteediting.com/onlinedocs/barmitzvah.pdf
http://www.interfaithfamily.com/file...tzvahguide.pdf
Bar Mitzvah Speech from Parents
http://www.justwriteediting.com/onli...barmitzvah.pdf
Academy BJE : Adults (http://www.bje.org.au/adults/templateBase.php?id=1070&gid=2 - broken link)