Here is Teto, a creature known as a fox squirrel which Nausicaa befriends. He is often seen riding on her shoulder, in both the manga and the anime.
In the anime Laputa: Castle in the Sky we also see what appears to be the exact same creature:
Do the two stories occur in the same universe?
From reading several articles across the internet I would have to say this is a fan theory only and not borne out in any direct quote from Studio Ghibli or Miyazaki himself.
This article directly addresses whether multiple Studio Ghibli films are set in the same universe or narrative and conclude this is not the case:
There is no concrete evidence that all the films exist in the same world, though minor characters do cross over.
Having visited the Studio Ghibli Museum in Tokyo and having seen some of Miyazki's notes on exhibited story boards for Spirited Away where he notes that the background female faces in one scene can all be basically the same to keep down production costs, it is clear he is a pragmatic film maker. The appearance of Teto in Laputa is an easter egg and nothing more. If you look closely at his other character designs, Muska from Laputa bears a resemblance to the father in Totoro. The Laputa robots have their design origins in Lupin the Third made 18 (?) years before Laputa. Meanwhile the makkuro kurosuke from Totoro reoccur in Spirited Away. It is too much to ask that all these films make up one mega-text.
For the sake of completeness the following links are the other articles I consulted.
