Birthdays are the most common reason jewelry is given, which is exactly why most birthday jewelry is forgettable. The pieces that stick are tied to something specific about the year.
That can be as small as a birthstone, a number, or a reference in the note. It does not need to be expensive to be specific.
Is a birthstone piece a good idea?
It is, if she likes the stone. Some birthstones are loved and some are politely tolerated. If hers is one she never wears, choose by metal and shape instead and let the message carry the birthday.
When should I order to arrive in time?
Order earlier than you think you need. Give yourself a buffer of at least a week beyond whatever delivery estimate you see — a birthday does not move, and a late gift feels different from an early one.