When this item first debuted, the duster, hat, and scarf were sold as Samantha's Travel Outfit. The parasol, stereoscope, and mirror & brush were the Travel Accessory set. Later on, the accessory set was retired, and the parasol became part of the Travel Outfit, the stereoscope became its own separate item, and the mirror & brush set became part of Samantha's bridesmaid accessories set.

So, no, the parasol was not part of the travel outfit in the very beginning. But it was later on, after the accessory set was retired.