You definitely don't need the artwork in place before you get your business structure/DBA setup. I would say to go ahead and do things in steps.
Register yourself as a business. After that, you can find an artist to work on the design you have in your head.
I've used designoutpost.com, rentacoder.com, and elance.com to outsource projects. I think for what you're describing, any type of freelance artwork sourcing place will work.
As for if they "charge alot", that's sort of a relative question
If this character or design is the basis of your t-shirt line, then it seems like a pretty important piece of the puzzle. How much is that worth to the success of your business to get it done right? $5? $100 $500 $1000 for a lifetime of sales of that design.
Think of it as an investment in your business. I've seen artists charge anywhere from $10 to over $1000.