There are two things in the sentence that can be confusing.

1- The verb used by the author is aller chercher (to fetch) and not chercher (to look for).

Ayant cherché would mean “having looked for”, and not “having fetched”. The important thing here is that le Petit Prince went to fetch the watering can and whether he had to look for it or not is irrelevant to the author.

2- In compound past tenses être can be used instead of aller when one has gone somewhere and has already come back. Some consider this usage as incorrect but great authors have used it and not only Saint-Exupéry.

So the sentence could have been :
« le Petit Prince, tout confus, étant allé chercher un arrosoir d’eau fraîche, avait servi la fleur ».
But not :
« le Petit Prince, tout confus, ayant cherché un arrosoir d’eau fraîche, avait servi la fleur »
because the meaning would be different.