Anyone that has a serious vibration should have it checked out. However, before you get to far into suspension and new tires, try having your tires trued. Tire truing was very common years ago and there are still two alignment shops here in Clarksville, TN that do it. It's about $7.50 -$10.00 per tire.
For those of you who have never heard of this, they spin the tire on the vehicle and shave the tire with a device similar to a lathe. When they're complete the tires are perfectly round and balanced.
The manufacturing process of car tires has risen to a level of quality that in most cases would never require truing. However, large tires still can suffer in manufacturing and be slightly out of round. That in combination with flat spotting in a cold morning can make for a bouncy ride.
If you suffer from uneven wear patterns due to poor alignment and failure to rotate, this process can also help you. Once a wear pattern is established there is nothing you can do to change it short of truing. Once you've trued the cupped tire it's new all over (minus tread wear.)
If you have large oversized tires from lifting your truck this is almost essential! I guarantee you’ll love it when you get it back!