My 27 year old son and his girl friend who are serious are invited to his first-cousin's wedding. I wanted to know the etiquette on if she should give a shower gift or not. As far as I know she has not been invited to the shower. Thank you,

She should wait until she is invited to the shower. Only shower attendees are obligated to give a gift. You might think, "Well, she wants to give a gift and does not feel obligated to do so" but the bride will feel guilty for not inviting her to the shower and if she finds out that a gift is coming, she might feel obligated to invite the girl.

A nice wedding gift should suffice.

Chi-Japanese Food, Thank you so much for kind response it was very helpful. Norene