2005 Chevy Silverado 1500, 4.8 liter V8

Sorry to hear that. 
Personally the travel trailer idea is a poor idea based on your previous posts. But yes your truck will haul that camper on the bumper if you take it really easy. 

Is it advisable? Nope

is it safe?  Not really but people have done dumber stuff. 

Will it break the truck? Not likely unless it’s already ready to blow up or fall apart. 

Will the bumper hold? That’s a solid maybe. Depends on what you encounter.  

I’ve towed 10s of 1000s of miles and hundreds of different trailers. 
couple weeks ago was the first time I’ve ripped a trailer tongue off the stinger. Hit a bad bump the wrong way on a forest road doing about 6mph and bam. 
But the strength of the bumper is only half your problem. Since you have no idea how heavy the tongue weight is and I have no idea how clapped out your truck suspension is, it may just bury your suspension on the bump stops. Which is a host of other concerns. 
Back to the task at hand, go very slow and say a prayer and there’s a 69% chance it’ll be fine. Once anyway. 
But based on what you’ve divulged so far, being motorhomless requires moving frequently. So take your lessons learned from the first move and apply them forward. 

And no, there’s no straps or things of the like that will help the bumper.