Yeah, once you start taking on the Witcher contracts and side missions, you'll be leveling up much faster. Just remember to take your time, because it's a long ass game (I think I took over 120 hours for my first playthough
).
Something to keep in mind... aside from completing missions and contracts, drawing energy from a Place of Power will also give you one Ability Point, so it's good to find them around the maps. At this stage, I'd recommend placing most (if not all) of your ability points towards upgrading your magic skills (Igni and Aard are good choices for now). Igni works great for burning drowners and in the fight with the Griffin, too.
Also... get rid of your Witcher armor set as fast as you can, and find some better clothes. I think there are some treasure chests around in White Orchard that'll give you some.