I've forgotten, is Gimli older than 80 year old Aragorn?
I cannot remember reading it, but my gut says "yes".
It was only the word "laddie" that seemed out of place to me, not so much his accent. Although, I have to say that I thought Gimli and Treebeard sounded identical. But I think that's because I knew ahead of time that JRD speaks both. Glen had no idea until I told him and didn't think they sounded alike at all.
I did a quick look through the Tale of Years, and it didn't have an entry for Gimli's birth... but! I stumbled across the Dwarf genealogy at the end of Appendix A, and it gives the year of Gimli's birth as 2879... which makes him 11 years older than Bilbo, and ~52 years older than Aragorn.