Your syntax for qualifying operator names is a bit off. In order to refer to Vect's cons, (Data.Vect.::) won't work, but Data.Vect.(::) will. I also really enjoy that you can omit the Data. from this, leaving just Vect.(::).
When qualifying an operator's name, we also can't use it infix, so rather than x Vect.(::) Nil we need Vect.(::) x Nil.
Beyond that, the type-checker will probably help get you back on track.
Error: While processing right hand side of transposeMat1. When unifying Vect m (Vect len a) and Vect m (Vect ?len (Vect 1 a)).
Mismatch between: a and Vect 1 a.
ListDisambiguate.idr:6:62--6:74
2 | transposeMat1 : Vect n (Vect m a) -> Vect m (Vect n a)
3 | transposeMat1 [] = ?createEmpties
4 | transposeMat1 (x :: xs) = let xsTransposed = transposeMat1 xs
5 | xMapped = map (\x => Data.Vect.(::) x Nil) x in
6 | zipWith Data.Vect.(::) xMapped xsTransposed
^^^^^^^^^^^^
Cheers,
Alex