Skin to skin isn't the same as babymooning. Babymooning AFAIK is spending time exclusively in the company of your baby to the exclusion of others people and things (ie shutting yourself away from the MiL and having time to get to know your infant).
Skin to skin (kangaroo care) is exposing your baby to your skin to encourage bonding through the release of oxytocin which is created by increased nursing frequency and also as a reaction to the warmth of skin to skin contact.
It's all bollocks though, it used to be called 'motherly love' but I guess that didn't sound pompous enough for some
I don't think a baby moon is that awful a term. I think it is probably the honeymoon term it is derived from. New husband/wife and you spend some time away from others with just them. New Baby and you spend some time away from interferingfamily well meaning folk with just your baby.
Not my most favoured word, but it does describe the concept of retreating to your bed with the baby, and not thinking about housework/cooking/entertaining/going out at all for a couple of days and just giving them the chance to feed and feed. Different to skin to skin bonding.
Do think it's weird the way we need a term for what would have been not even commented on in the past. Are we becoming so aloof as parents that we need to label normal care and attention with special terms?