I'm assuming you are an Italian citizen? Residency and citizenship are two different things. If you aren't an Italian citizen, you'll have to tell us what citizenship you hold.
Assuming you are an Italian citizen, you can apply for a working holiday visa that will allow you to live and work in Canada for six months (not 2 years - those from Italy are only entitled to 6 months). It's really not possible for any of us to say how easy or difficult it will be to find a job once you get here.
Extending the work permit will likely be very difficult since the employer will have to give you a full time job offer and also go through the LMIA process to get an approved LMIA (this is a long and expensive process for the employer that requires them to prove no Canadian could be hired for the role). I think it's unfortunately quite unlikely an LMIA will be approved for a beautician job.