Confusion in applying for AdSense

As per Google rule and policies, your site must be at least 6 months old and the domain ownership does not matter. Even if anyone tries to apply for Adsense through the sister site of Techulator i.e., Indiastudychannel or any other such article sharing website, the website is owned by someone else, yet Google verifies your account and you can earn through it.
Other necessary requirements for approval of Adsense accounts are that your blog or site must have at least 100 unique visitors daily. Your site must have high quality content written by not copied from any other sources.
The quality of the content is very important because it not only helps you to get better Google ranking and gain more traffic but it will also ease the Adsense approval process.
Write atleast 10-15 articles, promote your site and once you start getting the required traffic, apply for Adsense.

You can apply but make sure that your (old blogspot) new custom domain blog has enough articles / contents before proceeding to apply. Not only this, there could be some other parameters at the moment which we might not aware, but the usual old procedure has to follow to avoid any disappointment.

You can also try to use 'Author Bio' and contact detail on your blog. Make sure that your blog has enough organic traffic as well beside quality content. Likewise, there are few points to remember before applying. For your question, yes you can apply. However, do not get disappointed in case Google rejects your application, you can apply later (after few months gap) like second or third time to get its approval.

Google adsense has its own method of verifying ones site for contents and the traffic to them. They expect good quality contents like articles and that also at least 10-15 articles.

Another thing is since when the site is active. If it is a new site then it is difficult to asses its performance with such a low statistics. Generally they will require that site is active for at least six months.

One thing which is very important is volume of good contents in your site. More such volume with good keywords will definitely attract more traffic as search results will display your site frequently.

There are multiple ways to apply for the Adsense here.

1. Own domain and hosting with content. With the ownership of the domain and the content more than 6 months to 1 year. Then you can apply and wait for the approval. Here make sure your website has enough large content worth applying.

2. YouTube channel. Here your channel needs to have 10,000 views for entire channel. Once achieved you can apply for adsense. And if already have adsense then you can connect existing with the adsense account.

3. Blogspot and other hosted adsense. Here you can get based on the hosted adsense rules. Blogspot domains do get approval and later you can add your domains after getting manual approval from them.

Your case falls into third type.

You have domain and the blogspot with content. So you can pretty much apply to the adsense from these two criteria alone. It's possible to get the approval. But make sure you have enough content. Often denial is either based on the domain ownership and the content length too. So find out what applies for your case and work accordingly for the approval.

See there is requirement of six months before applying for AdSense but it is not followed strictly. I had seen a lot of friends getting approved for websites less than a month old. Here are some points you need to consider before applying:

1) Make sure that there are at least 20-25 quality posts on the website.
2) If the blog is getting organic traffic of about 200-300 page views a day, you will certainly get approved.

All the best.

As the other members have rightly said, Google AdSense will not disapprove your request solely based on the domain which is not older than 6 months. It is the website or blog content that should be more than 6 months old. So, if you have the decent amount of organic traffic from Google and from other search engines, you will be given approval with the new domain of your existing blog or website.