Yeah, 6kitten is right. It's a lot easier to go from a degree to a PhD in the sciences/Engineering but for social sciences, it might be a lot harder.
I also finished a degree and will be commencing a PhD soon (should've been this month if not for my supervisor's incompetence!) Well, the month's not over yet, so I’ll have to see.
If your supervisor thinks you're able, then go for it. They have obviously evaluated your skills and trust them enough to handle a PhD.
All the best.