Remember that the "max tow rating" of 1500lbs, assumes that you also factor in all the calculations into the GVWR for the entire setup. Doesn't actually mean you could tow 1500lbs.
You have to take the GVWR of the car (usually on the placard sticker by the driver's side door) then subtract the curb weight of the car (should be listed in the owner's manual - generally assumes "wet" weight, ie, all fluids, but no gasoline) and all the weight that is going into the car (gas, tools, yourself, passengers, etc.). Whatever is left, is your available towing weight.
Example on my car (rounded some numbers to make math easier) - GVWR is 3500lbs. Curb weight is 2250lbs. Weight of a full tank of gas is 80 lbs @ ~6lb/gallon. Weight of myself + all junk in and on my car is about 270lbs.
3500 - (2250+80+270) = 900, that means my maximum towing load can only be 900lbs.
Not really the speed that should or distance that will be an issue, you really have to get that trailer balanced just right - ie, make sure the tongue weight is within the limit of the trailer hitch. Highly recommend running an auxiliary transmission cooler (assuming you have an automatic transaxle) - if running a 5-speed, make sure your clutch is in good shape.
Also, that much weight, you'll likely need some sort of load distribution hitch - not sure expensive, but is an additional cost. Trailer should have some sort of braking system, that weight will overwhelm your car's brakes fairly quickly, even with updated friction material.
Springs and struts will likely get beat up pretty good. You can minimize this impact by making sure the trailer load is balanced.
I hear that you are trying to save up some money - but there is a reason why most landscapers and lawn maintenance folks use trucks or SUVs - a FWD economy box like the Corolla will work really hard with something like this.
Personally, I tow with my 2002 atleast once a year, sometimes approaching my max trailer weight of 900lbs - most of the time the weight is much less, but my distance traveled is further. The car can handle it, but you will be shortening the life of some of the suspension and brakes. Driving dynamics can be downright scary - you are adding a fair amount of sail area behind the car that seems to catch any breeze at all. Some times, ride was fine - other times, white knuckle driving.
With the OEM stuff - brakes didn't even make it a year, burned them up under 20K miles. Struts and springs were damaged pretty quickly. Struts didn't leak, but they didn't dampen as much as they used to. Springs really sagged under the weight and were permanently distorted. I switched them out to TRD springs (sport spring, higher rate, but lower ride height) and KYB GR2 struts. The struts will need to be replaced again, but the springs are still looking OK.
With my 4-speed automatic - I installed an auxiliary cooler when I got it from the start - coupled with aggressive fluid replacement intervals when I would tow and pretty short intervals when I don't, the transmission has held up pretty well.
You 9th gen is a little different than my 8th gen - your 2007 model is geared slightly higher, as the engine has its powerband moved further up the revs (8th gen are geared lower and have a bigger power bump at low RPMs). The later 9th gens also have DBW throttle, so be careful and try and get as smooth as input as you can when pulling the trailer. EBD (part of the ABS system) that should be standard on your car will be a big help, as it can detect an offset load like that, and shift brake effort front and rear. But you'll have to inspect the brakes pretty regularly to make sure they have enough meat left for the job.
