I'll qualify my criticism here, I spent over 14 years as a body shop owner, and spent the last year teaching auto body. All told I have been involved in the Auto Body industry since 1979, although my degree is in Automotive Technology, most of my career has involved painting, bodywork, or frame straightening/diagnosis.
I respecfully disagree, if a shop quotes you less than 1000 to fix that, RUN don't walk to your truck and leave. If someone quoted you $200 to do a timing belt replacement what would you think?
Secondly, that dent won't pull out using studs, the corner is way to strong, you will end up with a bunch of holes in your sheet metal. That said, you are on the right track, that 1/4 panel does not need to be replaced. It can easily be repaired by a qualified tech, who would first push it out from behind, then hammer, and possibly use a nail gun(studs).
A 1/4 panel replacement would cost in excess of $3K, don't go there! Expect to pay $1500 minimum, unless you have them blend or tape a hard line to avoid going over the roof. I'm talking about a shop with a building, who pays rent, insurance, permits etc. Someone doing it in the back yard could obviously do it for a lot less.