Hii Yickkk
let me say that Im excatly in the same position as yours
for my case, my project is my idea, and no one in my lab has worked on it..nor my advisor is much aware of it..im yet to make my mark in research field with any sort of publications...(this is my 39th month of PhD)...I have to do everything by myself...there are nobody in my lab who are expertise in my area...i will be SOLELY responsible for the success and failure...
inspite of all this..i feel itz better to work on our own project...since after completion..u can proudly say that..yes it was mine..and mine only......

best wishes cris...
even if they say some comments take it in a postive way and improve your paper based on that..im sure you will be fine

Congrats Fluffy..good job