Should I list 6 weeks of job experience on resume?

So I am new grad LPN and about 6 weeks ago I started a LTC position. I am not new to the LTC care world as I worked as CNA . The facility that has allowed me to start my first LPN position sucks! It just really isn't the place for me. I know jobs are scarce especially for new grads, but I feel like in the mean time I could turn in my resume to a couple of places and see if I get any bites. My question is should I put recent LPN position on my resume or just leave it off and start over as a new grad?? Any thoughts???

Thanks!
What kind of a reference from your supervisor do you expect? Six weeks is kind of long to pretend it doesn't exist unless your probationary period is 90 days.
My probationary is 90 days. I honestly would expect a good review as I have had no write ups or issues, I haven't called in or been late. They have told me that they are impressed with how quickly I have been able to take on 25 residents and often the more experienced nurses have come to me for a second opinion or help.