as you get to larger tanks, catching the fish later when issues appear becomes harder and harder. if you are tempted by the QT-bug (a good thing), you really should start it out completely right from the beginning and ensure you have strict protocol going forward. Even if you don't see any classic signs of Ich or other issues, they still could be present and your fish are just doing a good job at combating it to keep it from overtaking them.
Dipping won't do much for anything. Tank Transfer Method (TTM) for fish to eliminate any possibility of Ich being present and PraziPro to eliminate flukes and other worms are your two best initial remedies to ensure your new 130 DT stays clean.
Your course of action depends on what you did to setup your new DT. Did you add anything wet from any other source (whether you believe that source to be clean or not doesn't matter)? Such as live rock, macro algae, used equipment (that wasn't cleaned and dried well before you used it), coral, CUC (hermits, snails, etc), etc.
Assuming that something was added, for 100% assurance that you start out right, you should leave that tank fallow (fishless) for 11 weeks first. This will let most of anything bad carried over die off, such as Ich and most other parasites. Many people skip this step, but many people get burned by skipping it too... really up to you, just depends on how much you want to avoid issues down the road.
Starting about 4-8 weeks before that, you should perform TTM on the fish, and then house them in a separate tank until the DT fallow period is up. You can do PraziPro while they are in this temporary tank.
Going forward, you will want to TTM all your new fish before adding them to your DT.
Optimally, you would fallow treat all your new non-Fish (literally anything wet) going forward for 11 weeks. Again, many people just dip and skip this step. Some succeed, some fail.
The most important thing is to get into the strict protocol of treating and observing your fish before moving them to your DT. That alone will save you many headaches! It really isn't that much work to go the extra mile on non-fish though.