First off, don;t do it like that! Never concatenate strings to build a SQL command. It leaves you wide open to accidental or deliberate SQL Injection attack which can destroy your entire database. Always use Parameterized queries instead.
When you concatenate strings, you cause problems because SQL receives commands like:
SELECT * FROM MyTable WHERE StreetAddress = 'Baker's Wood'
The quote the user added terminates the string as far as SQL is concerned and you get problems. But it could be worse. If I come along and type this instead: "x';DROP TABLE MyTable;--" Then SQL receives a very different command:
SELECT * FROM MyTable WHERE StreetAddress = 'x';DROP TABLE MyTable;
Which SQL sees as three separate commands:
SELECT * FROM MyTable WHERE StreetAddress = 'x';
A perfectly valid SELECT
DROP TABLE MyTable;
A perfectly valid "delete the table" command
And everything else is a comment.
So it does: selects any matching rows, deletes the table from the DB, and ignores anything else.
So ALWAYS use parameterized queries! Or be prepared to restore your DB from backup frequently. You do take backups regularly, don't you?
You know what a parameterized query is, so why suddenly start to ignore them?
Second, ImageConverter.ConvertTo doesn't change anything - it returns a new object of the requested type. You need to save that reference, and pass that to your DB, not the ImageConverter instance itself:
ImageConverter converter = new ImageConverter();
byte[] data = (byte[]) converter.ConvertTo(im, typeof(byte[]));
...
cd.Parameters.Add(new NpgsqlParameter("@qr_code", data));
But ... why are you faffing about with a DataAdapter to do an insert, and even trying to use Fill on it? I'm pretty sure that won't do what you want it to ... No SELECT for the DataTable to get any information, no instruction to actually do the INSERT.
Use a Command object with the INSERT instead, and then call ExecuteNonQuery on that.