I'll add my two cents worth, because I just went through all of this myself.
First- I called and arranged an inspection appointment with the WSP. The DOL told me I wouldn't be able to get the transit/travel permit until I had the appt. arranged.
Second- I went to the DOL and picked up a transit/travel permit, which was good for two days. I didn't have to pay for it when I got it, since they said I would pay for it when I came back after having the inspection.
Third- I drove to a State Certified public scale (they are listed on the DOL website) and had the trailer weighed for $10. They gave me a receipt showing the weight.
Fourth- I drove to my appt. at the WSP. I spent the majority of my time there talking with the inspector about teardrop trailers.

He and his wife want to get one, so we had a good time talking about them. I don't think he ever even checked my highway lights to make sure they were working! He did measure the trailer and ask for information about the axle. He also looked at the receipt for the axle.
Fifth- I went back to the DOL with my receipts in hand (all of them), my slip from the weight station and my paperwork from the WSP. The woman had a freak-out that I had so many receipts and told me that I had to go and make copies of all of them for her! ARGH!!
Sixth- I went and spent over an hour making copies of all of my receipts.
Seventh- I went back to the DOL, talked to a different person there, and he started to say that I didn't need all those copies of receipts. I was about ready to lose it on them when he said this!!! Finally, he took everything and issued me a temporary plate (since I chose to get a personalized one), and sent me on my way.
I am still waiting on my Title to arrive, but I am going to give them a couple more weeks before I start bugging them about it.
So, there ya go. Not too terrible a process, except for the whole making copies of all of the receipts issue!
Good luck getting it taken care of.