FindmyPast have a marriage (wrongly ascribed to Llandegfan parish) between Robert Dooding (Llaneilian) and Catherine Hughes (otp) at Llandyfrydog on 6 Aug 1796. Both signed by mark and the witnesses were Griffith Hughes and Hugh Williams.
There are also a number of baptisms in the Amlwch and Llaneilian parish records which are summarised below:
Doodin (surname), Cathrine (forename), 1790 (baptism), Thomas (father), Jane (mother), Llaneilian (parish)
Doodin, Elizabeth, 1802, John, Elin, Llaneilian
Doodin, James, 1794, Robt, Anne, Amlwch
Doodin, Joseph, 1784, Joseph (miner), Grace, Amlwch
Doodin, Margaret, 1811, William, Anne Williams, Llangoed - illegitimate
Doodin, Mary, 1778, Joseph, Grace, Amlwch
Doodin, Mary, 1780, Joseph, Grace, Amlwch
Doodin, Mary, 1780, Thomas, Margaret, Amlwch
Doodin, Rose, 1778, Thomas, Ellin, Amlwch
Doodin, Thomas, 1799, Jones (James?), Jane, Llaneilian
Doodin, William, 1797, Robert, Ann, Llaneilian
Dooding, Catherine,1796, Robert, Cathrine, Amlwch
Dooding, Mary, 1784, Thomas, (blank), Llaneilian
Dudding, Elizabeth, 1800, Thos, Eleanor, Amlwch
Dudding, Grace, 1799, Robert, Catherine, Amlwch
Dudding, Grace, 1799, John, Ellin, Amlwch
Dudding, John, 1791, John, Ellin, Amlwch
Dudding, John, 1801, Robert, Catherine, Amlwch
Dudding, Margaret, 1792, Robert, Anne, Amlwch
Dudding, Margaret, 1800, Robt, Ann, Amlwch
Dudding, Thomas, 1806, Robert, Catherine, Amlwch
Dudding, William, 1792, Thos, Jane, Amlwch