Calculate specific heat of a substance given other information
Your equation is correct, as are most of your measurements.

The unit for $c$ is $\ce{Jg^{-1}K^{-1}}$ if using grams as mass, ($\ce{Jkg^{-1}K^{-1}}$ if you convert the mass to kilograms).

Using your formula, however, does not give the answer you gave. When calculating using a calculator, consider that a parenthesis needs to be put around the denominator, as such:

$$c = \frac{q}{(m\Delta T)}$$

or else the calculator takes it as being $\ce{979J / 20g \times 45K}$ which gives the value you got.

It needs to be $\ce{979J / (20g \times 45K)}$ which gives an answer that is much more reasonable.