"Republic of Texas: Poll Lists for 1846," compiled by Marion Day Mullins shows:
Beatty, E. -- Cass Co. Beatty, John -- Cass Co.
Foster, J. -- Cass Co. Foster, T.J. -- Cass Co.
Cass Co, TX was formed from Bowie Co. in 1846, so for the marriage record you may need to check out Bowie Co, TX, too.
In 1861 county name was changed from Cass to Davis and in 1871 it was changed back, so be aware of those county names, too.
Have you checked land and probate records for John or E. Beatty?See if Elizabeth shows up as an heir?In 1850 there is a T.J. Foster in Cass Co., but it looks like his wife has died.If it was your Elizabeth, then watch for her children showing up as heirs to her portion of any estate that would have been left to her.
I would also look for county histories, families there that early should at least be mentioned, and you never know what might be included for "pioneer" families.