The Manned Dragon capsule, the Dragon 2, is designed to be able to do a powered escape from a launch stack. That requires at least 1.1 Gees thrust (and ISTR a requirement of 3 Gees). Further, it's designed to perform a powered landing after escaping the launch stack. But it's also required to be able to detach in flight at any altitude, including LEO, and perform a controlled descent to soft landing on a hard surface..
The Dragon 2 capsule has "120,000 pounds of axial thrust"... 60 tons, for an easier measure. (Note that each of the 8 superdraco motors is capable of 8 tons, but due to angles, 3.5 of the 64 tons of total thrust is non-axial (a fancy way of saying sideways), and the rest is throttled back for safety reasons.
At liftoff, the Dragon 1 masses some 26,000 pounds (including 6000 pounds payload capacity); the Dragon 2 probably masses around 30,000 pounds (15 Tons). This means that, on 2 engines, it is probably capable of 1G of thrust.
Two superdraco engines are required as a bare minimum for flight (due to load balancing), and preferably 4, due to the configuration of the thruster nacelles. Each engine has a 25 second duration on internal fuel (according to the wikipedia entry). Assuming that, as with other SpaceX engines, they can be throttled back to about 65%, this puts the minimum thrust to about 19.5 tons, or roughly 0.66 Gee, and possibly up to 38 seconds thrust.
If we assume even deeper throttleback (Elon Musk has stated a goal of 30%), then we could get this down to 10 tons of thrust, and up to about 80 seconds. And there are 4 such pairs.
The notes on the Dragon 1 capsule give an endurance on orbit of 2 weeks. The Dragon 1 is a parachutes-to-water design.
Also note: Earth landing requires 6 of the 8 superdraco engines working. So, if aiming for earth return, either refuelling or limited use are required.
On the Moon
The moon's roughly 0.16 Gee gravity makes the Dragon 2 thrust an excess. In the case of hopping, this means it will do exactly that. Assuming the exhibited 65%, it's going to have to use bursts.
Landing from Earth orbit requires at least 2 pairs. That leaves room for landing and a few hops on the moon. dry-landing on earth is likely to need well more than that.
The capsule itself seems, from the very limited data available, to be suitable for this role.
The capsule, however, relies upon the trunk for the solar panel connections. Those are not a suitable fit for the landing, unless the trunk is fitted with landing gear.
Further, the capsule door is some 6' off the ground when landed. Use as a taxi would require a ladder.
In such a taxi use, the total of about two hundred seconds of thrust and lack of solar panels would necessitate a support infrastructure.
Noting that NASA gave about a 25% above minimum delta-V, as a safety margin. The total delta-V on the Apollo LM was about 15,380 feet per second, just a hair over 4.7 km/s total delta V. Low Lunar Orbit (LLO) to Lunar Surface is about 1.8 km/s delta V.
The best estimates of current Dragon V2 delta V put it around 1.6 km/s delta V. On the other hand, the capsule itself is rigged for external fuel connections, in addition to its internal fuel, so a modified "landing trunk" is a very real possibility. Adding a trunk with another 3-4 km/s worth of fuel, and some landing legs and a ladder, and you have your down-and-back, with the majority of mass beneath the center of thrust (which is a fairly stable condition).
Note that LEO to Earth surface needs about 4.3 km/s of delta-V... most of which Dragon is slated to achieve by drag from Aerobraking. (Versus the Apollo CM, which did it all by drag - first by aerobraking, then by parachutes.)
It could be pressed into such a use. It would not be optimal. It's not actually designed for this role.