D

Step 1: Recall the definition of the magnetic dipole moment ($\vec{m}$) for a current-carrying loop. The magnetic dipole moment is given by:
$$\vec{m} = I \cdot A \cdot \hat{n}$$
where:
- $I$ is the current flowing through the loop,
- $A$ is the area of the loop,
- $\hat{n}$ is the unit vector perpendicular to the plane of the loop.

Step 2: Analyze the direction of the magnetic dipole moment. It is perpendicularly directed to the plane of the loop, following the right-hand rule.

Step 3: Determine the proportionality. The magnetic dipole moment is directly proportional to both the current and the area of the loop and is specifically perpendicular to the plane of the loop.

Based on this analysis, the correct statement is that the magnetic dipole moment is perpendicular to the plane of the loop and proportional to the area of the loop.
Therefore, the correct answer is D.