I have no experience with hauling a PT on a single-axle, but I've trailered one over 1,000 miles on a 14' dual-axle. I also have quite a bit of experience hauling other garden tractors on a 12' single-axle, however.
You'd certainly be borderline on a dual axle, but they pull far, far better than a single. If you were willing to pay the price for an aluminum dual-axle, you could just barely get under that 3,000 lbs with an attachment or two. You can get aluminum 12' or 14' trailers that weigh about 1,000 lbs. In comparison, I have the 14' version of this steel one, and it weighs right at 1500 lbs with the spare...
Hawkline Trailer
Before I bought this trailer, I strongly considered getting a 12' single-axle to replace the old 12' snowmobile trailer I'd been using. My neighbor, who has MUCH more trailer experience, kept telling me to go to the 14' dual-axle as a minimum. (He recommended 16' or bigger.) I finally chose to go with the 14' dual, and am glad I did. With a weight distributing hitch, this thing tows like a dream... even up to 70 MPH or so.
Back to your question, IMO you need at the very least a 12' trailer (PT with just a bucket on it) or better yet, 14' trailer (PT with a mower deck on it). Either of those, as a single axle, is going to require you to get the "balance" exactly right or you'll be putting too much or too little tongue weight on your hitch. Then there's the issue of brakes...
A dual-axle would work much, much better -- especially given the rear-engined PT... and a 16' trailer would work even better, allowing you to load several attachments and the PT. IMO, if you're going to be hauling it farther than across town, spend another couple hundred and replace your hitch with a Class III hitch so you can pull a bigger trailer -- IF -- your tow vehicle is rated to tow more....
Then, get at least a 14' dual axle, with electric brakes -- which will cost an additional couple hundred for the brake controller, installed. Give serious consideration to a 16' -- because it'll only cost about $100 - $150 more, and won't weigh a whole lot more either....
I just pulled my PT-425 from Mass to Tenn (900 miles) on a 14' trailer with a 60" finish mower deck, 48" rough-cut mower, 60" rake, and small HD rock bucket -- all on a 14' trailer. But, I had to stack the implements, and stand the finish mower deck up and strap it on to the siderails. A 16' or 18' trailer would've made it much easier....
BTW, I also had a boxblade, grapple bucket and minihoe in the bed of my pickup, so I was very close to my legal CGVW on a Dodge Dakota. My 2 cents, your mileage may vary...