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In my opinion moving in is NEVER an option when dating. When partners move with another, they are opened to each others lives much more intimate then dating and frequent seeing. It ruins the thought of marriage because the guy has everything a. Marriage has. WITHOUT the long process and getting on a knee.
More direct to your question, 2 months is early to be talking about a key. It's not a top priority of his so it must not be needed. I say wait at least 4-8 months of you two dating. If he gives you the key then you can keep it, but you don't have to be at his house every other night.