Can you do a Garter stitch on double pointed needles?
Yes.
Assuming you still intend to work in the round, you'll need a stitch marker for the start of the row. You'll need to ironicly alternate between plain and purl each row. Otherwise you'll just get stocking stitch. 

If you intend to work flat which given the pattern is garter it probably is. I would recommend cables over DPNs.