Is ferrous sulphate ionic or covalent?

It is both!!!

FeSO4 can be separated into the ions Fe^(2+) and SO4^(2-)

That's the ionic bit.

For the sulphate anion (SO4^(2-)) the atoms are covelently bonded with in the ion. As best I can demonstrate S(=O)2 - (O^(2-))2 . That is two oxygens are doubly bonded to the sulphur and the other two oxygens are singly bonded to the sulphur, leaving each of these singly bonded atoms with a '2-' charge on them, for ionic combination.