Yes, you need to use a towing-compatible tune to tow - whether it's 1000 lb or 5000 lb, it requires the use of a towing-compatible tune. Why? Because towing means towing, and towing use means you need a towing tune.
And since you are going to be towing that frequently, you basically should leave it on a towing-compatible tune all the time - you do not want to flash the PCM a few times a week, that would be hundreds of flashes every year and that isn't smart. So if you are going to be towing several times a week, my advise is to leave it on a towing-compatible tune instead of flashing it back and forth constantly.
The most popular combination of tunes is an 87 octane performance tune, then a premium gas towing tune, and a premium gas performance tune - that way, between the stock tune and the 3 custom tunes, you have towing & performance tunes for both regular and premium gas, so you have the most flexibility. That is what I would recommend for you as well.
Now there are some people who, once they feel how the truck runs with our tuning, *never* want to run on the stock tune again, and we can certainly understand that, I feel the same way - so another choice for your situation would be to go with an 87 Octane towing, 87 octane performance, and then a 93 octane performance tune.
The thing to remember in your case is that for towing, you need to use a towing-compatible tune. Now that being said, if it really were just 1500 lb, and it was on flat ground and for only a short distance, then you probably could get away with doing *that* on our performance tuning and still have safe EGT's - but as soon as I say that, someone will turn around and tow 3000 lb up and down hills, etc on their performance tunes - people are people and will push things beyond what we recommend all too often, we find - so we have to say that for *any* towing, use only a towing-compatible tune.
I hope that I've managed to help you more than confuse you with this!