Yes, it is correct.
I did the same thing, ran a 60a circuit to my garage, and I regret to
this day that I did not make it a 100A circuit.
Spend a few more bucks and get a 100A circuit. You can then buy some
large equipment (welding, plasma cutters) and run them inexpensively.
If this is THHN/THWN wire in conduit you can use the 75c column of
310.16 (65a). If you are using a non-metalic cable NM-b or UF-b you
are specifically limited to the 60c column (55a) but you can still
"round up" so 60a breaker is OK either way.
You can't use the 90c column (75a) because the breaker terminations
are only rated 75c. The 90c column is generally only there for
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