Contra @groodythehobgoblin's answer, the size categories probably should act as ersatz age categories.
You tagged this dnd-3.5e, so I'm using that monster manual. The 3.0 manual had different numbers, but a similar relationship.
What we are looking for ideally is an entry for "Monstrous Scorpion" with an advancement entry that says "1 HD (Tiny), 2-3 HD (Small)..." etc. That's missing, so this is not a purely read-and-interpret answer.
What we actually have is a bunch of entries that read "Monstrous Scorpion, [Size]". The advancement for each only lists a hit die range (and only for the larger ones), not a size change. Read strictly, that suggests that the different sizes are totally distinct species of scorpion. Every "Monstrous Scorpion, Huge" pops into existence fully-formed as a huge Vermin with 11HD. If that is correct, you're good to go already: the egg is probably unpleasantly large for transport, but as soon as the immature scorpion hatches, it's ready for training and riding.
However, I note that breaking the sizes into different monster entries is far easier to use as a DM, which may be why WotC chose to present it this way. I also note that the size ranges don't overlap. So, stacking them up, we get:
- 1/2HD: Tiny
- 1HD: Small
- 2-4HD: Medium
- 5-9HD: Large
- 10-19HD: Huge
- 20-39HD: Gargantuan
- 40-60HD: Colossal
...which is a remarkably clean progression. Were I running your game, I would use that progression as though it were a single monster with that in the Advancement block.
(In fairness, the progression is not quite as clean for other, similar vermin. E.g. treating the centipede like this means it's missing an entry at 2HD).
However, there is also another piece you're going to run into pretty fast: how do Vermin advance? Nominally every 4 HD adds 1 CR, which suggests that your scorpion needs to be gaining HD four times as fast as you are gaining levels if it is going to keep up with you. I have no advice on how to a handle that other than talking to your DM.