Yes, always bury your waste, and do it far from the creek or springs. The ground in the DCHS area way from the water can be hard, but with proper effort (it's worth it, to keep the creek clean!) a 12" hole can be dug. The toilet paper has to be buried that deep, or the coyotes or other animals will just smell it and dig it up. Or bring a small lighter with you and burn the paper (the dry part will burn easily and you can bury the rest). I know that sounds gross, but it really is not as bad as it sounds. I always keep some toilet paper and a lighter in a zip lock baggie, to keep them both together and to keep the paper clean. And quickly biodegradable paper can even be purchased at many RV dealerships, camping supply stores, etc.
Regarding shovels, the small plastic trowels that cost about $3.00 are very light weight, fit easily into any part of a day pack, and work perfectly. You can get them at any Big-5, R,E.I, Sports Chalet, Walmart, etc.