You'd need to add RAM for Perl and your programs to run in. You'd need to add some form of non-volatile storage big enough to hold Perl. You'd have to write some sort of VM (if one doesn't already exist) since these boards are designed to run programs from the onboard EEPROM instead of from the external memory. This doesn't sound like the way to go.

Have you considered using a computer with a Mini-ITX form factor motherboard (such as Via's EPIA mainboards)? This requires much real estate, and probably requires a fair chunk of power (possibly requiring a house's or a car's power outlet), so I don't know if it meets your needs.