search a record by Date

<apex:page controller="DateRangeCont">
 <apex:form id="dt1">
 <apex:pageBlock >
 <apex:pageBlockSection >
 <apex:pageBlockSectionItem >
 <apex:outputLabel >Start Date</apex:outputLabel>
 <apex:inputfield value="{!a.From_Date__c}"/>
</apex:pageBlockSectionItem>
 <apex:pageBlockSectionItem >
 <apex:outputLabel >End Date</apex:outputLabel>
 <apex:inputField value="{!a.To_Date__c}"/>
 </apex:pageBlockSectionItem>
<apex:commandButton value="Go" action="{!go}" reRender="dt"/>
</apex:pageBlockSection>
 <apex:pageBlockTable value="{!customer1}" var="ct" id="dt">
<apex:column headerValue="Customer Name">
<apex:inputField value="{!ct.Name}"/>
</apex:column>
<apex:column headerValue="billing city">
  <apex:inputField value="{!ct.Billing_City__c}"/>
  </apex:column>
  <apex:column value="{!ct.createddate}"/> 
  <apex:column headerValue="billing postal code">
  <apex:inputField value="{!ct.Billing_Postal_Code__c}"/>
  </apex:column>
</apex:pageBlockTable>
</apex:pageBlock>
 </apex:form>
</apex:page>

public with sharing class DateRangeCont {
    public list<customer__c> customer1 { get; set; }
    public datetime startdate1;
    public datetime enddate1;
   public customer__c a { get; set; } 
    public DateRangeCont(){
     customer1=new list< customer__c>();
    a=new customer__c();
    }
    public PageReference go() {
    startdate1=a.From_Date__c;
    enddate1=a.To_Date__c;
    customer1=[select name,Billing_City__c ,Billing_Postal_Code__c,Createddate from customer__c where Createddate>=:startdate1 AND Createddate<=:enddate1];
    return null;
    }
}