I don't know about recurion in XS (C), but you can save a little bit of time by recoding your traversal algorithm to avoid array dereferencing. Something like the following (untested):

# object1:
sub depth{
    my $self = shift;
    my $max = 0;
    foreach my $item ( @{$self->{child}} ) {
        next if ! defined ($item);
        my $depth = $item->depth();
        $max = $depth if $depth > $max;
    }
    $self->{myDepth} = $max+1;
    return $max+1;
}
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