Keep in mind that the weight of the camper (and the mfgr's number) is usually for what amounts to an empty unit....heck, they seldom include the weight of the television or microwave:(
Loading up the dogs, luggage, and DW (no, I'm not being a smart*ss:B) may also put you over limits.
More than likely, you will be fine, but keep an eye on the tire inflation numbers during the trip...you will be close to max. Also, adding the better tires and wheels will help the tires and wheels, but won't do anything for the axles and drive-train that the weight numbers are designed for.
I am by no means an expert on this.....I'm sure others will have better information....just tossing in my two cents....though I'm afraid that it may just confuse you even more.
Merry Christmas!! Welcome to RVing!!:)