From the research notes of Pam Wilson <wilsonpam@mindspring.com>:

Northumberland Co, VA Court Records 19 May 1703, page 246. Wm. Arledge and Alice his wife acknowledge a deed for 50 acres to Hannah Neale and Mrs. Hannah Neale acknowledges a Deed of 50 acres to Rodham Neale.

Alice apparently witnessed her father's will, according to this abstract [need to secure copy of original will]:

Northumberland County Will of Charles Fallin dated 17 Dec 1700, proved 16 April 1701. Sick and weak in body. To son Dennis Fallon land adj Saml Webb's spring branch. To sons Charles and William. Wife Jane sole extrx. Wit: Benja Browne, Else Fallin, John Hogan. Proved by oaths of Browne and Hogan. Re-recorded 19 Mar 1711/12 by William Fallin. 17.159 [Beverly Fleet, Virginia Colonial Abstracts, Vol. XIX, Northumbria Collectanea, 1645-1720 (Balt: GPC, 1971]

Else Fallin must be Alice--but if she was his daughter, why was she not named in the will??

Records that she died April 19, 1727 are obviously incorrect. This seems to be the date of death (or rather, the date of estate administration) of William's second wife, Sarah.