I'd recommend replacing the missing edging on the door before painting. There may be a slight difference to the paint finish between the laminate and the timber if you don't. You can use the Custompine 21mm x 10m White Iron-on Melamine Edging. The edging is ironed onto the door and then trimmed back to size with a sharp knife or chisel.
Please let me know if you need further help or had questions.