In theory, I think you could get by with the existing trap but it seems to me that you are going to have a hard time making the connection to the existing trap. I think you are going to have to run a pipe up the wall behind the pedestal sink and put the trap between the sink and the wall. Do you have access to the pipes under the floor? Is there an existing sink close by?
I have a pedestal sink with a trap and the line runs behind the pedestal and thru the floor and connects to the drain pipes below. This is a very old unusual design (I think) as most pipes would now be run in the wall behind the sink. In my case, that wall is brick so the pipe had to run straight down thru the floor.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13