Wot's a sensible age...

[Daeothar]

This poses a nice conundrum

I've been browsing the Boardgamegeek website for dungeon-like games with (plastic) miniatures, and they do not go further back than around 1985. Older games usually had either cardboard chits or meeples of some sort.

So the games I came up with that come close to your description are either Dungeonquest and Warlock of Firetop Mountain.

But the included minis are not in different colours, and I don't spot any female characters either. Which is not to say that those versions do not exist. In fact, I did see later comparable games (outside of your time window though) which did have coloured minis and male and female versions of the characters...

[Dubar]

Chances are the game I had was Dungeonquest.  All I can honestly remember is that my oldest daughter (under 10 at the time) routinely kicked everyone's butts every game, my son would stomp off when she won.

[Harry Faversham]

All I can honestly remember is that my oldest daughter (under 10 at the time) routinely kicked everyone's butts every game, my son would stomp off when she won.

Kind of reminds me of my lad's first game with the Dynamic Dunderheads.
He started as 2nd Lieutenant 'Johnny' Hero and ended it as Major Tantrum! He threw such a strop, I bonked him on the melon with a measuring stick, then dismissed him from the fields of glory. Miserable, grassing, little git came back with his mother in tow and all us 'little generals' got a rocket!


 

[Dubar]

LOL!  My youngest grandson (7 today!) got out of throwing fits when something doesn't go his way a while back and can now give as good as he takes.  The little rascals learn quick!