Want sort of size are you after?  And for what purpose (i.e. how strong does it have to be?
DavidO

Would this be for an Easter project? Maybe for a float?
Thin cardboard can be rolled and cut, then taped into an egg shape. Then you could layer paper stips or mash over it for strength. Paper strips would give you a snoother finish, but mash would be much faster and you can still achieve a pretty smooth finish.
Or you can just go with chicken wire or hardware cloth. Hard to deal with, but would be fairly easy to shape. (Just wear gloves!)  You would then have to layer paper strips over the wire. I prefer to work with mash, so I would do several layers of paper maybe 6-10(?) then go over with a half inch layer of mash. On big projects like this I make a huge batch and then divide it into smaller batches. I take a smallish batch (a big double handful) and roll it flat between two sheets of wax paper, or even newspaper. I then brush glue on the surface to be covered and apply the rolled mash, blending as I apply each new piece. The mash will fill in any lumpiness that may occur from layering the paper strips.
Either method you use, it's going to be big job LOL.

What about the ambient temperature and humidity where you live?  If you are able to dry the material easily, there may be a better way, which has already been discussed elsewhere in the Forum - but it bears repetition.
DavidO

OK, so at the moment you certainly don't have drying outside but later in the year it can be warm and generally dry.   What we have looked at before is laying laminate over a former and sand (or soil) is probably the easiest.  A hot, sunny day on a local beach would suit you well!!

Or, if you have a dry garage with a source of heat . . .
Cut two cross sections for your egg from strong card or MDF.   One will be the full length, the other is half of the width.   Make two of each and keep the second pair for later.

Join the two together (glue/tape/etc) and fill in to the shape of half an egg.  The cross section pieces will help guide the shape.
What do you fill in with?  Sand - it would have to be moist to hold shape;  Clay - it would need rather a lot;  Paper - screwed up and from large pieces, finishing with smaller - might be a slightly lumpy finish. 
These are just examples; you would need to choose the medium that will achieve the finish you want.

Over damp structures, lay clingfilm.  You can then lay the paper you want for your egg over this to the thickness you need and leave to dry.

Make the other half and join them together.

It would be best to experiment with something much smaller first to see what method works best for you.  Please keep us posted as to how you get on.
DavidO