Carrots!? How unexpected...
Yes, we often, as new owners, mistake their communications. Once we finally learn to speak " dragon" , the bonds begin to form quickly.
If we closely observe them, and spend plenty of time with them, they teach us THEIR language! With my beloved Dez, I had as fluent a converstion as with any human. All day, on me or off, in his cage or on his window perch, we spoke. He also had many sub- sonics, that I could not hear, but felt as vibrations, like a cat who purrs softly,and you feel it in his throat.
I worked at a rehab in a big zoo, and had a special friendship with an emu, who followed me everywhere. she started thumping her chest bones at me when I rubbed her throat. The keeper said, no that was a female, and only males did that to indicate an interest in breeding! ( yeah, I was turning on an emu. story of my lfe.) Well, the other female produced a viable clutch of eggs, come spring! ha, ha!
Those are the sort of sounds I often detected Dez giving me, especially when he was on me and very content.I suspect they speak to each other in sub sonics. I knew purring, humming,thumping,booming, and several others. I always kept two fingers on his chest and throat when I held him.
Now I have a new fellow, and we are working together to learn his language. It is very rewarding. And it deepens the relationship, as you have discovered.