US Navy Disaster Relief Task Force

We're paying for it now by having to re-task military forces away from their original missions. That's going to have to be made up somehow.

I'm just thinking that maybe dedicated assets could do a better job for around the same amount.

The problem there is what dedicated assets?
Each disaster is different and requires a different approach and different assets.
Pakistans was localised, distribution required helicopters and land transport, while the bulk shipping could use the countries ports and the main airports were unaffected. The regional US bases(and deployments) could be used together with assets already there.
The christmas tsunami on the other hand was very widely dispersed it hit different areas to different extents, that meant that a very varied set of assets was required operating from a wider variety of areas.
Now if you look at this one in Haiti, its localised and needs a whole different set of assets and approach using a whole different area of deployment.

It just isn't practical for the US to have a dedicated agency with all the assets it may need and a handy way to get them to all the places it may need to go.