I wouldn't use Libc at all here; the Julia standard library Dates in conjunction with TimeZones package is far more functional and featureful. First, parse your date as a timezoneless Date:
julia> using Dates, TimeZones
julia> format = dateformat"Y/m/d H:M:S"
dateformat"Y/m/d H:M:S"
julia> dt = DateTime("2020/10/26 11:08", format)
2020-10-26T11:08:00
Then append the local time zone:
julia> zdt = ZonedDateTime(dt, localzone())
2020-10-26T11:08:00-04:00
Finally, you can ask if there will be any future transitions — and what they are:
julia> show_next_transition(zdt)
Transition Date: 2020-11-01
Local Time Change: 02:00 → 01:00 (Backward)
Offset Change: UTC-5/+1 → UTC-5/+0
Transition From: 2020-11-01T01:59:59.999-04:00 (EDT)
Transition To: 2020-11-01T01:00:00.000-05:00 (EST)
Note that the concept of "Daylight Savings" isn't explicitly encoded into a timezone — there simply exist variable timezones that change which constant offset they're in at given times. You can see in the above output that I'm currently in UTC-4, but will be switching to UTC-5 on Sunday.
So if I wanted a simple function that asked if there is an offset from my normal timezone, it'd look something like this:
julia> is_offset(zdt::ZonedDateTime) = zdt.zone.offset.dst != Second(0)
julia> is_offset(ZonedDateTime(dt, tz"America/New_York"))
true
julia> is_offset(ZonedDateTime(dt, tz"Europe/Berlin"))
false
So right now, New York has an offset from its "standard" timezone (and we call that offset daylight savings), but Berlin does not (it transitioned back yesterday)