Why don't you gather all the evidence you can and apply for a tourist visa for your GF? (By evidence I mean if she can show strong family ties to Romania, owns property there, has a good job that she has to go back to etc). If it's granted she can come here, you can marry and then apply for PR from within Canada and you won't have to be apart. You would need to apply for PR before her tourist visa runs out and if you apply for an Open Work Permit (OWP) at the same time, then she won't need to extend her tourist visa as she will have implied status until the OWP is granted.
The first step of the PR process is "Approval in Principle" (AIP) - this means you have been approved to sponsor her. This usually takes a few months from the time you apply (if doing inland). If you include the OWP application with the PR application, you put it in a separate envelope and mark that you only want it processed once AIP has been determined. What happens is you'll get the AIP and OWP at the same time and then you no longer have to worry about her "tourist" status in Canada and your girlfriend will be able to work while you wait for the rest of the application to be processed.
If you can't get a tourist visa for her then you'll have to go to Romania, get married and then apply for PR. It does mean you'll be apart for a while but it's usually faster than in-land to reach the end of the entire process. Bucharest gives a timeline of between 4-8 months.
Hope that helps.