crickets are great, and there are many safe insects and worms they can have as well. I'm not sure about carrots, I believe they need to be mashed for dragons. You could try a softer vegetable instead, such as tomato. They also like bok choy, arugula, collard greens, cilantro - it would probably be easier to tell you what they DON'T eat ha! :lol:
I would recommend googling "what do bearded dragons eat" - I have had a lot of luck with the first link.
Kevie gets cilantro, tomato, acorn squash, cucumber, and every now and then a bit of fruit, like strawberry. However, her main food is crickets because they need a lot of protein while growing.