Use either fetchrow_hashref or selectrow_hashref and extract the keys.

my $hashref = $sqlexe->fetchrow_hashref();
my @column_names = keys %$hashref;
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Update

My vote is for the NAME attribute of the statement handle (next reply). Thanks, pfaut.

If, like me, you've been indoctrinated into thinking that a class's interface should consist solely of methods, you'll miss a lot of good stuff that DBI makes available in the form of attributes.