Crowns often get replaced in servicing, if a correct replacement crown with the Omega logo isn't available a suitable replacement is used. Because ladies watches are not all that common in that era it could be that it was too difficult to locate a correct small crown to fit that watch. Its up to you whether you replace it but finding the part may be difficult (or not I really don't know).

 

The crown is no big deal, but you would not have mentioned it if it did not bother you. I would get a new Omega crown. This is not difficult and should be inexpensive with the right watchmaker. Even if it is not the exact style that came with the watch, there are many Omega crowns that would work and look good on the watch.

 

nice choice of watch by the way, rarely do you see a lady with a clean 1960s vintage Omega

 

You can easily do yourself and not mess it up and you can easily do it yourself and mess it up. You will have to cut the stem to correct length and remove any burrs. Once the stem is cut, if you cut too short, you will need another one. I would put some loctite on the stem and thread the crown on tight. let it dry. Do NOT use super glue.
Or go to a watchmaker, if he screws it up , it's on him.