The odd snap certainly came as a surprise to fans with the pretty brunette writing underneath: "People are so weird about breastfeeding in public, especially when it's not your baby!"
While Ms Porter (33) tweeted the snap as a joke, it has fuelled speculation that his wife of just three months may be getting broody as she settles down to married life with Chris.
If children are on the cards for Dawn and her husband, the pair may just turn their sights to Ireland and the prospect of raising a family here.
Roscommon native Chris has already spoken of his desire to settle down in Ireland in the future if his wife can be convinced to relocate across the water.
"I like the idea of it but someone might need to be convinced," said Chris, who currently lives in London with Dawn.
Any suggestions of a move to Ireland appear to be off the table for the moment, however, as Dawn announced that she is looking for a "small family house to rent in Bristol".
Dawn took to Twitter this week to ask followers for suggestions for a new home in England, revealing she had already been in touch with estate agents and is in the market for a quick deal.
"Desperately on lookout for a nice, small family house to rent in Bristol. Anyone out there looking to rent their place out immediately?" Dawn asked her almost 200,00 followers on Twitter.
Scottish-born Porter, who has made a number of documentaries for BBC3, married Chris in August 2012.
Chris was recently back working back in Ireland for Sky series Moone Boy, and his new film Calvary, which also stars home-grown talent Brendan Gleeson and Aidan Gillen.