The only Dodsworth serving in the Light Brigade was Schoolmaster-Sergeant Frederick Dodsworth, Regt No. 771 who spent the entire war at the Cavalry Depot in England.
That said, however, I should point out that there were members of many other regiments who were present at the battle . . . and men who received clasps for Balaclava.
I recommend joining the Crimean War Discussion Group at Yahoo Groups . . . he could have been a member of the Heavy Brigade (who also charged that day), the 93rd Highlanders who made their bold stand known as the 'thin red line', the Royal Horse Artillery. . . just to mention a few.There are experts there with extensive records . . . and most live in the UK.One of them may be able to point you in the right direction.