Translation:Can I copy that picture?
Using も is the more "proper" way of doing it, yes; and should be used with people like teachers or doctors, or even people you just met.
For anyone who may be curious, the も in this instance would mean something along the lines of "even if." So literally it would be "Is it (です) good (いい), even if (も) I make a copy (コピーして) ? (か)"