Transfer Mail from one Gmail Account to Another Gmail Account?

[TexasDudeUSA]

I've seen people ask this question multiple times over the year(s) that gmail has been open but there's never a clear answer. I know that you can get mail from other mail accounts but not Gmail to Gmail. I have an old Gmail address I want to collect all the e-mail from and delete it once it's empty. I've tried doing a task of downloading as much as I can from the old e-mail onto thunderbird and then using a redirect add on but Gmail limits my sending per day, so the process could span over 100 years! What should I do? (Other than keeping both e-mails)