Welcome to DF!
Warning: you'll get hooked--on dancing, on competing, and on DF!
The pice doesn't seem to be too out of line for a pro-am comp, assuming it's all-inclusive for entry fees, pro fees, etc. Does it include meals?
One way to keep comp costs low is to go a la carte, if your studio allows it. By paying for each element separately, you have better control over costs. There are some comps I can drive to, so I don't stay in the hotel. When I travel, I often compete in only one style, so I only need to stay in the hotel two nights and don't get the meal package. My pro is great about finding ways for me to compete inexpensively (relatively, anyway).
I would think twice about incurring credit card debt for a comp, unless you're *sure* you can pay it off within a few months. If you like competing, you'll want to do more, and what then? More debt? Not a good idea.
If competing will be a one-time or once in a blue moon thing, I'd consider waiting until you got a little more dance experience. Have you participated in any studio showcases? That is a good way to get your feet wet and do a "dress rehearsal" for competing. For me, anyway, I have more confidence and enjoy a comp more when I feel confident in my dancing and have had some live-audience experience.
BTW, what is a DVIDA studio? My studio uses the DVIDA syllabus, but AFAIK, isn't affiliated with DVIDA in any other way. Are they starting a chain?