Moving to CO from another state in a month, how do I go about switching my car insurance? ?

Moving to CO from another state in a month, how do I go about switching my car insurance? ? I'm under my dad's insurance now (AAA).. it's his and my car on his policy. I was told by them that once I cancel it, it'll take effect immediately and be taken off the policy. I'm moving to CO on the 18th of next month and want my new insurance (USAA) to take effect on that day. If I start my policy for that day and cancel the AAA the same day, will AAA pro-rate June's insurance so I don't have to pay for the full month since my car won't be insured by them for that whole month? I just don't want to get stuck paying the bill twice in one month for both companies.

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