Deposit and first month's rent one month prior to move in?

[Kraig Krueger]

I'm renting out my second property, and have a qualified tenant that is ready to sign a lease.  They won't be moving in for a month.  Their lease will start in June.  I was planning to collect the security deposit when they sign the lease this week.  Should I also be collecting the first month's rent, or wait until just before they move in a month from now?  Thank you in advance!