Backpacking is something that happens a lot in the Philippines and the local people have grown accustomed to seeing it. Ease of transportation makes it easy to get around. Travelling solo is absolutely OK, but since the places you are going to will be filled with travelers, both foreign and locals, you probably won't be alone for long.
Filipinos may be surprised to see a solo female traveller by herself, but this is more of a concern due to their culture, rather than an actual danger that is there. Be confident in travelling solo as a female in the Philippines.