I would recommend a foam roller perm if you want to get one. Rather than it looking poodle-like, it will be a softer curl.
There are regular perm rods that are large, but I think your hair would be too heavy and those curls wouldn’t stay in as well. Foam roller perms are going to create a curl that looks like…Taylor Swift curls.
Since I haven’t seen your hair, if you go in for a consultation and they suggest something different- go with what they say. But from what you’re telling me and me not seeing it, that’s what I would suggest. I’ll post a picture below of what the perm would look like. Good luck, and let me know if you have any more questions.