Yes you need a job offer to apply for their nomination.. Here is the text taken from their site....
Skilled Worker Program Nominee Criteria
1. A score in the vicinity of 50 on our Self Assessment form, (PEI-PNP-01-SW) - we recommend after completing the Self Assessment, the candidate undergo a credentials assessment as education and training requirements may need to be upgraded. Assessments for Designated Trades
2. Education and training consistent with the position offered - having your credentials assessed to Canadian standards for regulated occupations, (Regulated Industries in Canada) is strongly recommended as education and training requirements can differ greatly from country to country.
Visit Citizenship and Immigration Canada for more information.
The Prince Edward Island Newcomers Association also has information on this issue, and other services to help people get settled in Prince Edward Island. info@peianc.com
You will find additonal links below under Foreign Credential Recognition for Professionals and trades.
3. A bona fide offer of employment from a local employer - Once you have a bona fide offer of employment from a local employer, please complete the Pre Assessment Form (PEI-PNP-02-SW) and submit it to this office for review. A bona fide offer of paid employment, at prevailing market rates, from a Prince Edward Island employer is a requirement for our Provincial Nominee Program. The job must be in your field of study and/or experience, and the employer must be able to prove they have been unable to fill the position after advertising both provincially and nationally. Please note, you may be asked to visit Prince Edward Island for a pre-employment interview.
4. A moderate command of English, and/or French language if required for the position.
5. The intention to settle in Prince Edward Island - At the request of the company, the Prince Edward Island Provincial Nominee Program Office will support issuance of a temporary work permit (from Citizenship and Immigration Canada) to allow the prospective immigrant to accept employment and to assess whether the applicant and their family will be able to settle successfully in Prince Edward Island.