"It takes eleven months."
十一月 (じゅういちがつ) is November. 十一ヶ月 (じゅういっかげつ) is eleven months. The extra character in there distinguishes that it is a counter for the number of months, as opposed to which month of the year.
I'll add to this and say it's also written differently.
Do you still use ヶ月 if the number of months is not a whole number from one to twelve? In other words, is ヶ月 used only to avoid ambiguity?
Not sure what you mean by avoiding ambiguity, but if you wanted to say something that's not a whole number, you could say, for example, 二ヶ月半 (にかげつはん) to say two and a half months.
How do you type this small ヶ character with the windows Japanese input method? (And on Android?)
I just wanted to add that, in general, you add the smaller characters by typing "x" followed by whatever it is you want to be small. If the first result isn't the character you need, tap the space bar until the correct one appears. I have an iPhone, but the method is generally the same...type "x" before the character, and then choose the right one from the list.
Still the same keys. Both L and X allow you to type small kana. It's not like japanese keyboard doesn't have romaji...
What I do on the computer is type out the number of months with the counter (いっかげつ, にかげつ, さんかげつ, and so on) and hit the space bar until that character appears. (Not sure about Android, I have an iPhone.)