The difference between 10's, 12's and 13's, is about one inch in height from a 10 to a 13 so no it is not beneficial imo.
There is one guy who comes to Florida and uses a tow dolly with a pair of 12's on the rear of his 10 incher.

66S. A Uhaul 12x6 with a drop down gate is around $50 a day plus a drop off fee in a different town, just don't tell them you are hauling a Mini in it or on any other Uhaul product for that matter. Their tow dollies and car trailers are not much more but the main problem with Uhaul equipment is it is heavy and according to their website the 12x6 trailer weighs the same as a car trailer at 2200 lbs so you need something substantial to pull it.
What you buy trailer wise depends on if you need it when you get to Utah.
If you are considering flat towing a long distance maybe consider removing the axles and letting the car free wheel.
Sorry to hear of your Daughters medical issues and hope she does well with the Chemo.

https://www.minimania.com/msgThread/123211/1/1/Ping__StGeorge__Utah

Hugh, if you look at some of my other posts like the one above you wouldn't be asking the questions you ask.  Now, I have checked out the St. George mini scene, have seen the Coke Moke, the Police car, the Mk3 'S and the countrymen - wood siding looked great, but then when his dad cut down the ash tree, had it milled, and make a very beautiful set of siding.
     But then the underlying story -  last November daughter was diagnosed with stage three breast cancer.  Since that time (a lot of time has been spent in St. George) Chemotherapy, surgery, radiation, and after all of that cancer has mutated and is now in lungs. So more chemo.
     Anyway, looking at options flat tow, dolly, trailer for the car,  will probably lighten the load by selling some blocks, parts, etc.

Red Riley thank you for your input - will look at craig's again.
     

5 x 10 or 12 ft utility/landscaping trailer. Buy one from Craigslist and sell it on later if you don't need it. That's what I would do.
atlanta.craigslist 5-by-10 trailer

So John, does this mean Salt Lake City is calling?

Regarding a tow dolly. Any thoughts on it being beneficial to mount 13" wheels on the rear if its a long trip? For those of us who are running 10"'s  

john..  I recommend a tow dolly.. bought new one locally about 10 years ago..  for $599.. works great..  only thing I have done.. is replace tyres once an tow strap twice..  later bc

Thank you masal this is the kind of input I need

I would not put any more weight on a HF trailer than a shell for the same reasons as Hugh stated and they just don't look that strong imo.
Any full size tow dolly will work but on a long 2k mile trip with maybe suspect tires a trailer is the best way to go.
You can buy a decent 12 x 6 trailer for around $1200 and sell it on when you arrive.
I have looked at Aluma aluminum trailers and they make a single axle 750lbs tilt trailer with no ramps to deal with starting at around $3200, these trailers seem to have excellent resale.

Yes, that is an option, as is flat towing.
I looked at an RV last week where the queen bed cranked up and you could drive the Mini into the back.
But then trying to check out all options 

As a Mini is 52" wide at the front, I'd suggest a bit wider trailer. It's altogether possible that you could get by with the 48"wide trailer if you load it backwards....been there and done that. There is a few things to consider though. #1. If the Mini has an engine in it, it will be extremely tail heavy and you won't be able to go very fast without it fishtailing like a, well, you know. Also, when I loaded a Mini roller (without an engine) this way on a 4x8 trailer, it loaded fine until we got to the front wheels. They would not fit between the upright railings on the trailer. As there was an F150 parked adjacent to the trailer on the left, and the person who was helping load had a brand new truck he could position on the right, we did a little stretch exercise. I put a strap around the top of the rail on the left and right, and hooked each one to the trailer hitch on the F150's. We ratcheted the sides apart until the wheels would clear the uprights. We gently backed the trucks toward the trailer and the uprights lodged themselves against the tires. Although very snug like that, we still tied it down. So, that's how you make it work, but I don't have a cure for the fishtailing without pulling the engine. Good luck! Of course, you could just buy a longbed pickup. put it in the bed and haul it to the destination. Once there, sell the pickup. Done deal! Of course, another option would be to call a friend who hauls Minis all over the country and see if he might be able to help. Just a thought...

Any contact info? Phone email snailmail?

Hugh, lets just say for example that I was going to move to a new location say 2,000 miles away (go west "young" man) and had a project Mk1 Austin Cooper 'S LHD that I purchased back in 2002 that has been sitting in my garage for the last 15+ years as well as a few spare parts to move ...(you have seen the basement so you know how few parts I need to move).  So not to be confused with my 66 Mk1 Morris Cooper 'S that you refer to and has been running the streets of Atlanta since '96, as it was built 10 October 1966 and was a North American Export (so it's a '67). 

Now back to the original question:
I see Harbor Freight has a 4x8 foot 1750lb capacity folding trailer $499.99 - but what is out there what should I be looking for? 

I believe in the outside storage I have some bug-eyed Sprite hubs and misc parts.

John, If you tow your Mini anywhere she'll think you forgot how good she makes you feel when you drive her. TOWING???? Really? How many thousands of Miles have you put on that Mini? Towing, really? She's no trailer queen, she's a hard driving, original 66 Cooper S! Towing, really?

That was Tim Bossee in  Keterling Ohio

He made a great unit for around $1K

Big AL

After reading what is there about towing and not coming up with answers Ihave the following questions:
What tow dolly is there for a Mini?  Who makes them and the cost.
What trailer do you recommend and there again what price ranges.
I have flat towed Mini's several thousand miles - just looking for ideas.
Someone was using Sprite front hubs and making up a tow dolly.