To get a handle on whether this is reasonable, ask yourself the following question: For a given substitution rate and sequence length, how much time could pass without seeing any substitutions at all.
If I assume 5% per million years, that is 0.05% per 10,000 years. So for a 500 nucleotide alignment I would expect 0.25 substitutions in 10,000 years (along a single branch), and the probability of 0 substitutions would be about p=0.77. For 100,000 years the probability of 0 substitutions would be 0.08.
So assuming your alignment is about 500 nucleotides, your results don’t seem too crazy to me. If you want to be sure that the age of that cluster is younger you will need to sequence a longer fragment, and show that they are still identical over that longer fragment.
Cheers
Alexei