There is this baptism on Lancs On Line Parish Clerk site;
Baptism: 18 May 1788 St Bartholomew, Chipping, Lancashire, England
Ellen Parkinson - Dr. of Thos. Parkinson & Alice
Abode: Chipping
Register: Baptisms 1771 - 1791 from the Bishop's Transcripts, Page 19, Entry 2
Source: LDS Film 1656769
Robert and Ellen did have a daughter Alice, but I would have thought that Ellen would have named their eldest daughter, Alice - after her mother. This one's birth seems a little late from when they married.
Baptism: 18 Oct 1829 St John, Preston, Lancashire, England
Alice Worthington - [Child] of Robert Worthington & Ellen
Abode: Fishergate
Occupation: Accountant
Baptised by: James Gratrix
Register: Baptisms 1828 - 1832, Page 204, Entry 693
Source: LDS Film 1278755