If I play my Dazzling Aurora and get a Scuttle Crab, if I have over 11 XP and no unit at a battlefield, does Scuttle Crab go to base but ready, and can I move it to a battlefield or no?

No, you cannot perform a standard move with the Scuttle Crab in this scenario.

Here is the breakdown of the situation based on the rules:

1. Timing: Dazzling Aurora triggers "at the end of your turn." This occurs during your Ending Phase.
2. Standard Move Restriction: According to Rule 144.1.a, a Standard Move can only be performed during your Main Phase. Since the Scuttle Crab enters play during your Ending Phase via the Dazzling Aurora trigger, you are no longer in your Main Phase and cannot use the unit's inherent Standard Move ability.
3. State of the Unit: Even if you were in your Main Phase, a Standard Move has a cost of exhausting the unit (Rule 144.2). While a unit played via Dazzling Aurora enters "ready," the restriction regarding the phase remains the primary blocker for performing a Standard Move at that time.

In summary, the Scuttle Crab will enter your base ready, but you cannot move it to a battlefield using a Standard Move because you are not in your Main Phase.