I agree. Simply use this rail-to-rail op amp. I modeled this scheme. See the attached file.

 

I thought about this for a bit. I had a hard time coming up with a single transistor circuit whose output swings from near 0V to near 15V without a lot of distortion or by adding power supplies. ................

The op initially said he wanted to "amplify/boost" the output.
I missed where he wanted 0V to 15V.
Certainly you need a more elaborate circuit for that.