You can do this task with Erdas itself.
Convert the color coded image to vector by using raster to vector option under vector utilities tool. Convert the resulted Arcinfo vector file to shapefile using Import/Export option.
Open the vector file in QGIS. You can see the vector polygons corresponding to the vegetation class are coded as 1, 2, 3 in grid code field of attribute table. Calculate the area by using field calculator.
Hope this will help you.
