The Alabama Department of Public Safety Driver License Division is responsible for maintaining driver records and files. Once the clerk of the court enters the conviction notice to the Department, it may require 2 to 4 weeks for the entry to appear on the MVR. Keep in mind that over 1.4 million traffic tickets are issued annually, and about 800,000 of the tickets issued will result in a conviction. Only convictions are posted to the MVR, and not acquittals or dismissals. The Department's data entry unit will post this conviction to your record within a reasonably short time period.
you don't supply sufficient information to determine an answer. It could be a few days to a few months depending on the charging jurisdiction and the state DMV procedures. You can check your record by going to the local DMV office, or maybe even online. You are going to have to face the fact that you will pay higher insurance rates for the speeding ticket.
If they ask you about your driving history and you lie about it, you will have voided the coverage you purchased (and will be driving without insurance to boot). If they don't ask, they can jack the rates or drop your coverage (depending on the state law and the terms and conditions of the policy itself). It might have been better to look for new insurance before pleading guilty to the ticket, but that is water under the bridge at this point in time.