What is the best way to deal with whining?

It's the age my 11 month does the same thing. I'm home all day with them too. You can't really do anything at this age you have to wait for him to grow out of it. It gets better when they get more independent. Remember he's still new at everything so you are almost like a comfort or safety for him. I know it can be frustrating. Sometimes I just let him cry if I have something I need to do. He has to learn that I can't always be next to him because I have to get things done.

I don't think 13 months is too young to teach independence.  You don't want to have a child that starts having seperation anxiety when they start going to school because mommy isn't around.  My 11 month old will follow me around (I'm home all day too), but I try really hard not to always pick her up when she starts whining.  If she wants to follow me that is fine, but mommy sometimes has mommy things to do.  Sometimes giving her a book or something to occupy her while I am running around the house will keep her busy.  Sometimes they just need to cry.  Good Luck!

I've always told mine No whining when they started up with me.  I then would give them another phrase to say that would get them what they wanted.  They have to say it in a non-whining voice or they don't get what they want.  It doesn't work over night, but it helps.