If i moved in with someone in the future, what is the best month to do so for tax purposes?

Moved in together as in roommates or as in common law partners?

In a relationship moving in together for the first time, ultimately becoming common law.

Depending on your situation, there may or may not be any benefit to being common law. For example, if you have one partner with a high income and one with a low income, then the high earner might be able to claim the Spouse or common-law partner amount and lower their taxes owing. But if both partners have high incomes, then then living common law may not really change their income tax situation much.

If you don't have a child with your partner, you would have to live together for 12 months before you would be considered common-law So, if you do stand to benefit, then you would want to move in with each other as soon as possible.

One of us makes double what the other makes.  But both of us get returns. 

Then I would recommend talking to someone who can give you tax advice, like an accountant, so that they can look at both your finances and advise you on how you can make the most out of your situation.