All possible. twins where 1 when in Africa
 

Been with my 1 year old twins in Mali, Senegal, Guinea Bissau
Photography and Journey: Bamako to Casamance. Kafountine, Skiiring, Djembering.
Just on a trip up to North Cape now they are 3.5
Children go where u go.

Most of you (all, actually except for Markharf) are not answering the OP's question - she asked about crossing the Sahara Morocco-Egypt.
That is not like riding the tarmac to Bamako - Dakar with some offroad adventures on the way. 2010 is not 1978.
Perhaps she is just starting plans for a desert adventure and is not yet aware of the closed Algerian borders. Need to clarify your intended route, Karen. :)

There is a simple rule: if you are not sure about how to do it alone, do not try it with kids.

Rui

Hum, but you're never sure.....
RR.

I'd add that if its your first ever trip to the deep Sahara (i.e. not Moroc or the white desert in Egypt but southern Algeria for example), then it will be more risky with children. Better to have some experience first.