All trailer wheels have zero offset (or very nearly zero), so if you move from either 4.80-12 tires (actual width 5.0-5.1") or 5.30-12 tires (actual width 5.3") to 175-13 tires (actual width 6.7") the tire will be about 1.5" wider overall and that extra width will be split equally between the inside and outside faces. So to maintain the clearance between the tire and frame, you would need to use at least 3/4" thick spacers, so those 1.25" spacers would work.
But like les45 says, they will take a lot of life off your wheel bearings since the wheel will no longer be centred on the bearings. How much less life is hard to say, but you might need to replace the wheel bearings every year. As you seem to be using all of the capacity of your current tires (and maybe then some), you are probably already running the stock bearings near their limit, so you should certainly travel with spare bearings and enough tools to change them. At each stop, check the temperature of hubs to see if the bearings are overheating and about to fail. If they are too hot to hold, you have gone over the limit.
If you do buy spacers, be sure the inner bore of the spacer will fit over your current hubs as trailer hubs are often bigger than those of other vehicles (because they are zero offset, the wheel goes over the bearings, not outside them like in other vehicles).
It seems likely that bigger wheels and spacers would be a way of swapping tire problems for bearing problems.
Oops, forgot to add this link to
Carlisle trailer tire chart, where you can look up actual tire widths and diameters.