There is a coda and there is also a coda sign. They can be related but are different. A coda is an ending section or passage of a piece of music. A coda sign is a marker that is used to navigate within a piece of music, usually by jumping ahead and skipping measures. A coda sign may lead to the actual coda but it can also be used to jump ahead in a piece of music but not necessarily to the actual coda.
In your case the extra bars (regarding that, isn’t 2 bars and one beat actually 3 bars with the last bar being a quarter note and 3 bears rest?) are a coda but unless you need to jump to it from a non contiguous section there is no need to use a coda sign. A coda sign might even be confusing to some if there is no jump involved. A double bar wouldn’t be a bad idea though. You can also label it either with a rehearsal letter, or with the word “tag” or “coda” if you like, your choice.
EDIT BASED ON ADDED IMAGE:
Based on your added music, your best solution is to simply write out the 3 extra bars (a one beat bar is still a bar) rather than use a DS. A DS is usually reserved for larger sections in order to keep a chart from getting too long. Signs, codas, repeat signs and voltas help prevent charts from getting extremely long but they also can add an element of potential errors and confusion to a piece and should be used sparingly. It is much easier to just increase the piece by 3 bars than use a DS to go back such a short distance.
In order to literally write out what you have here you have to include one bar of 1/4 time. Here is a condensed version of what the final 3 bars would be and this would be added on to what you have written but without the sign and DS al fine:
I wonder if the 1/4 bar is what you intended or if the two 8th notes making up the word “final” are meant to be on beat 4 of the previous bar with the whole note instead, making the entire passage in 4/4 time. If that were the case it would look like this: