Doublets aren't all double-breasted. This is mine in blue velvet which is single-breasted and has tashes or Inverness flaps which are more flattering for the fuller figure -

You are probably thinking of this type of doublet known as a military or montrose doublet -

A jabot is a bit like a lace cravat and mine are antique maltese lace which I inherited but there are plenty of modern types such as Hamish is wearing. I know Kinloch Anderson sell them and I'm sure a lot of other shops will too. Can I just say though that a bow tie looks just as good with the single-breasted doublet as it is not buttoned up to the neck. I don't like the lace cuffs personally as I think they are impractical (dip in your soup etc.) and just a little bit OTT.