While this doesn't add on to anything for the "Is it Male or Female?" answers of previous (unless Doduo evolved in seasons later than Gen III), this does provide some solid explanation to the change in neck color.
You can see in the Gen I sprites that Doduo and Dodrio both have black necks, correct? If you need to see the sprites, check out this site for the information.
If you look at later Generations, you can see that Dodrio has had a change in neck color. Gen II and III had it as a white neck color. Gen IV and later split it so that Male Dodrio and Female Dodrio had different neck colors.
Now, Doduo was introduced in the Gen I seasons, of that I am sure. I'm not sure when it evolved (due to bulbapedia being offline at the moment) but there are some paths this can go in.
If Doduo evolved into Dodrio in the Gen II or Gen III seasons, then it can be either male or female, seeing as sprites were not split by gender back then.
If Doduo evolved into Dodrio in Gen IV seasons, then it is a female.
Edit: Thanks Kyron!
Turns out, Doduo evolved in a season that appears to take place in the events early in Gen III. As such, we cannot know the gender of Dodrio. However, if it appears in the later in the Gen V seasons with a white neck, it can be safe to assume that it is a female. If it is black, we can assume it is Male. That is if it appears ever again.