Magento 1 – Filter Based on Custom Attribute

I SAW LOT OF POSTS ON Stackoverflow & here also , I DIDN'T get SINGLE proper answer.

Hi dudes,
I have Filter option when i goto other Category->Product listing page .

I want to make it like Sort Dropdown of magento by default.

I have custom attr. as Carat for golden shop . I set its value from backend ,like 14,15 etc.

I m fetching it properly in drop down.

What should be done if i want to filter products by Carat ?

Till now my code to fetch Custom attr. & show in DDList.

    <!--Modified Code 27 Oct-->
    <?php 
        $name='carat_dropdown';
        $attributeInfo = Mage::getResourceModel('eav/entity_attribute_collection')->setCodeFilter($name)->getFirstItem();
        $attributeId = $attributeInfo->getAttributeId();                                    
        $attribute = Mage::getModel('catalog/resource_eav_attribute')->load($attributeId);
        $attributeOptions = $attribute ->getSource()->getAllOptions(false); 
    ?>

    <div class="sort-by">
        <label><?php echo $this->__('Filter By') ?></label>
        <select name="filterByCaret" >
                <option value="" >Select</option>                         
            <?php
            foreach($attributeOptions as $single){
            ?>
                <option value="<?php echo $single['value']?>" >                         
                    <?php echo $single['label']?>
                </option>          
            <?php
            }                                   
            ?>
        </select>
    </div>        
    <!--//Modified Code 27 Oct-->

DDList = Drop Down List.

Even in simple way

. Hi see, i have custom field in backend for jewellery shop Caret Value .So in drop down i will have all values i enter from backend for Carat Value like 13,14 etc. So in front end i want to show DDList ,and if i select 14 , products with Carat value 14 will be filtered &shown
Thanks for help.