Well, actually your dump truck probably needs USDOT numbers too as I imagine it is over 26,001 and you probably are towing over 10,001.
Remember, it's not just the ticket for not having the DOT numbers. They can then also ticket you for not having the rest of the DOT stuff! (safety inspections, log book, medical card, commercial insurance, etc). Sort of like piling on in football. I have no idea of what all they can do, as every trooper I spoke with had a different take.
On edit----------------
I think you may need to look into your requirements a little more. Unless your dump truck and trailer combine to less than 17,000.
PENNSYLVANIA-BASED COMMERCIAL VEHICLES
REGISTRATION REQUIREMENTS
Pennsylvania is one of 59 jurisdictions in North America who are members of the International Registration Plan (IRP). Except for Alaska and Hawaii, all other states and the District of Columbia are members of the IRP. In addition, the Canadian Provinces of Alberta, British Columbia, Manitola, New Brunswick, Newfoundland, Nova Scotia, Ontario, Quebec, Prince Edward Island and Saskatchewan participate in the plan.
The IRP applies to vehicles that operate through (interstate) or within (intrastate) any of the member jurisdictions and that are used for the transportation of persons for hire or are designed, used or maintained for
transportation of property. The plan covers motor vehicles with a gross weight or registered gross weight in excess of 26,000 pounds, combinations with a gross weight in excess of 26,000 pounds and motor vehicles
having three or more axles, regardless of weight.
http://www.dmv.state.pa.us/pdotforms/fact_sheets/fs-pacv.pdf
Also-
INTRASTATE DRIVERS operating a commercial motor vehicle with a GVWR - gross vehicle weight rating or GCWR - gross combination weight rating of 17,001 pounds or greater must have on their person, a medical examiners certificate or photographic copy stating they are qualified to operate a commercial motor vehicle. The driver must have been medically certified within the previous 24 months
Motor Carrier Assistance Program