Reference Column that Includes All Rows From Parent?

Say a table contains one column and three rows, respectively containing the strings ‘Cat,’ ‘Dog,’ and ‘Bird.’

If I create a blank table and set a column in the new table to reference the pet type table, then I can choose from a select list showing only those three values when manually clicking rows in the reference column.

I’d like a way to have the new table (with a reference column being added) automatically include a row for every pet type in the parent table.

Can it be done?

Edit: here’s a sample doc showing what I’m trying to do:

Trying to understand your request: so the two tables will have the same number of rows?