Nice pic and I agree that the border sets it off nicely.
Not sure whether, when you posted the pic you intended ithis to be an exact example of the issue - assuming you did, here goes.
Your picture (complete with border) is sized at 5.92 x 4.29
cm. Assuming you want to print this at roughly 6 x 4
inches (around 15 x 10cm), according to
PSE the maximum recommended size for "borderless" printing is around 13.064 cm x 9.478 cm. Although true borderless printing would be 13.784 x 10cm, if you want to print a non-white border, it's best to leave at least a little room as inkjets (probably more fairly, the inkjet owners) rarely feed the paper absolutely and perfectly straight and while you can trim a bit of white off, you can't stick a coloured bit that has been "trimmed" back on.
If you printed this all the way to the edge of the paper, any slight movement in the paper would result in the border being cut off somewhat. If, however, you size it to just below the maximum for one side (probably a bit more than the
PSE recommended size but a bit less than 10cm on the short size - say 9.8cm) - and keep the other edge in proportion, you'll get the best result.
I downloaded your pic, printed it resized as I suggest here, and it worked just fine, without cropping the black border (pixma i5000). The only issue is that because the picture size you have won't size proportionally to fill the paper - the extra half a cm of white space on each side of the black border on the long sides looks a bit odd - you could trim this though.
You might be better to prepare the border first at the exact size you want it to print, and then size the photo in on another layer to fill the middle although that may mean some of the pic will be hidden beneath the frame as, in order to fill the width in this case, the height is likely to go beyond the frame space provided. Because of Santa's chair, your height cropping options look limited though.