The Shaymen, who won the FA Trophy in 2016, booked their place in what is now the last 32 with Saturday's 4-0 win at home to Wrexham.
Fellow National League side Harrogate Town sealed their passage into the second round with the weekend's 3-2 win at home to Hartlepool United and Simon Weaver's side will be away at either Solihull Moors or Darlington in the last 32.
Should they negotiate tomorrow night's replay at Halesowen Town, National League North outfit Bradford Park Avenue will be at home in the next round against Maidenhead United.
Fellow National League North side Farsley Celtic side also face a replay at Altrincham tomorrow and a home clash against Barnet in the second round will await the winners.
Ties will be played on Saturday, January 11.
FA Trophy second round draw: Dorking Wanderers v Stockport County, Kingstonian v AFC Telford United or Leamington, AFC Fylde v South Shields or Southport, Royston Town v Hednesford Town or Chester, Solihull Moors or Darlington v Harrogate Town, Yeovil Town v Tunbridge Angels or Hampton & Richmond Borough, Ebbsfleet United v Kings Lynn Town,Bradford Park Avenue or Halesowen Town v Maidenhead United, Notts County v Sutton United or Dagenham & Redbridge, Chelmsford City v Eastbourne Borough or Salisbury, Torquay United v AFC Halifax Town, Eastleigh v Matlock Town or Chorley, Concord Rangers v Bath City or Sholing, Farsley Celtic or Altrincham v Barnet, Hornchurch v Carshalton Athletic or Aveley, Atherton Colleries or Barrow v FC United of Manchester.