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Just realize that the E or G ratings are generalizations and only the sidewall will tell you what the tire supports using a real number like 3042, 3420 or 3650 which is the lbs a tire will support. I've seen all three of these numbers on E rated tires so the E doesn't automatically mean one number. Generally, G numbers would be higher, but it's about the real number where it really counts.
Whatever the size, G rated tires will do better than E rated tires, like what you're planning but check the numbers to guarantee they meet your need and at what required psi.
When you say dealer, do you mean RV dealer? Be careful that the dealer doesn't charge you more for the convenience than what it might cost at a tire store, especially discount tires stores that have the best prices. If you are going to change out the tires, make sure you pay the best price and it might not be your RV dealer.
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