Might be tough to find just pieces for that size board.
I have a travel board with 1" squares and the pieces that came with it and the K is 1 7/8" . But you also have to look at base size, there is a guide in this sub forum where they point out the proper size for K height and base size.
Most travel set size pieces don't come with 2 Qs as far as I know.

I started playing chess in earnest only a couple months ago. I have a nice board for my home, but I would like a travel set, too.
Conveniently, I have an old and quite elegant travel backgammon set that has a chess board on the exterior. I'd like to get a nice set of wood pieces to go with it, but the square size is about 7/8". I'm having difficulty finding a set small enough - there doesn't seem to be much out there smaller than a 2.5" king, which I think is too big.
I would just buy any old travel set, but this particular board is one I picked up from a craftsman in Syria. I'd really like to find pieces to go with it.
These are the only 2" pieces I've found online (and may work), but they only come with 2 queens.
http://www.chesshouse.com/French_Staunton_Chess_Pieces_in_Rosewood_Boxwood_p/cp8375-dq.htm