What would you do in this scenario? You're a new graduate and this may be your only current opportunity to...?

Recent graduate with a BA in a certain field. I have a current job, which is not exactly utilizing the skills obtained through degree program. The company I work for uses a third party company for human resources needs. A new company which offers these services is setting up shop in our town and is soliciting us for business. I am to provide them with the needed documentation to provide us a quote for their services. Thing is- this company is the exact company I have had my eye on, wishing they had an office around me because it is perfect for my degree which I just finished last week. I have been searching high and low to find contact information for someone at this new office, which was supposed to open in early July but is now projecting to open August 1st due to delays, and I now have contact information for the individual who is soliciting the company I currently work for, for our business. Is it wrong to contact her to ask her if they are seeking personnel to staff their new office when it opens? If they are seeking personnel, it is the perfect opportunity for me, as a new graduate. What would you do? Do you think it is wrong to contact her (on my own time of course) to ask her?