Janis is here without her Arlo, but the cartoon is heading for what we’d have to call Arlo territory in the CIDU sense!
I thought farmer’s daughter’s tan a clever play on the familiar farmer’s tan but wasn’t sure what the intended extended meaning was or whether it has anything to do with farmer’s daughter jokes. But I thought it might help to establish it was a nonce coinage by pointing to many standard dictionary entries for farmer’s tan and the absence of any for farmer’s daughter’s tan. But couldn’t find any of even the former! But at the last minute, at least Urban Dictionary turns up with an entry for farmers tan!
Comics I Don't Understand 
A farmer’s daughter’s tan rolls the short sleeves up to move the tan line to the shoulders. Probably has nothing to do with the jokes…
Mark, thanks for noting the shoulders/sleeves. But let me point out Janis has also lowered the belt line of her jeans shorts. (And raised the hem of her top, together expanding midriff exposure.) Anyhow, even though there is no hint of a traveling salesman in the story, still it’s telling (but natural) for Janis to register a female farm resident by saying “farmer’s daughter” rather than, say, “farmer’s wife”. She just wants to think of herself as being young — and sexy, no?
I think it has more to do with her rolling up the bottom of the shirt to expose her belly, a la Daisy Duke.
With rolling of the shorts, midriff, and shoulders it’s not a farmer’s tan. Johnson might have called it a Farmer’s Wife’s tan, but elected to go with the younger, sexier, more familiar in humor Farmer’s Daughter designation.
Ironically, “farmer’s tan” is in the Urban Dictionary!
I am sure that “F-D-T” is just Janis inventing a spontaneous neologism for a feminine variation of the “farmer’s tan”. She’s willing to settle for that, since in April it’s probably too chilly for a bikini (or she’s too lazy to go get one), and she’s not about to “go commando” in a family newspaper.
Thanks, CWP(5), it took me a delayed second look to see the irony in that!
Arlo has always insisted that Janis not sun-bathe because he believes that it is unhealthy. Since she can’t wear a bathing suit in the sun without irritating him the best she can do is maximize the exposure with the clothes she has on. The farmer’s daughter tan is an amusing reference to a farmer’s tan.
Kilby, may I bring to your attention the Arlo and Janis strip from May 7, 1999?