Is it acceptable to submit a postdoc fellowship application (same lab, same project) to two funding agencies at the same time? I've already applied for one post-doc fellowship with one project with the consent of my possible future supervisor. I will know whether I've been succesfull in 6 months.

Now I realised that there is another fellowship to which I could apply - my potential host supervisor agreed that she would support me for both fellowships.

From my view I see no obstacles to ask for both, nevertheless I want to ask, what would be the opinion of a potential reviewer if he/she will get the same project for review twice from different agencies? If I will apply for both fellowships, both the review process and the results anouncement would run more or less in the same time period.
It's quite common to submit proposals to multiple funding agencies at the same time.  Most grant applications ask you if you are submitting the proposal to multiple funding agencies.  You should note this in your application.  If both agencies are interested in funding your proposal then they'll coordinate awards so that you don't get funded twice.