RNAi is a very interesting subject, and the importance of this relatively new discovery is highlighted in that the Nobel Prize in physiology and medicine this year went to two scientists who have really helped to elucidate what RNAi is and how it works. Wikipedia has an exellent, and well referenced, explanation of RNAi: http://en.wikipedia.org/wiki/RNA_interference
. I encourage you to read this carefully before proceeding.
As for projects - you will see that the best understood systems for RNAi are multicellular eukaryotes (though bacteria have perhaps a sort of similar system). As you note, it would not be feasible to work with mice. Depending on what grade you are in, what facilities you have, how much time you have, and people who might be able to help you - you could look into the possibility of using C. elegans (a little worm) or arabidopsis (a plant) for your studies. (With all live organisms - even for bacteria, you should check with your teacher to see what the rules are.)
You might also consider a bioinformatics type project - where you mine data available on public databases for information on RNAi.
If you are not wedded to the idea of RNAi, but in general would like to use a modern molecular genetic tool(s), you might look at some of the topic ideas under Life Sciences (e.g. biotechnolgy and genomics) on the Science Buddies webpages.
If you firm up your ideas a bit and still would like help - please post back.