Usually the only restriction on Money Market accounts is that you can't have more than 6 withdrawls a calendar month. Most have minimum balances to open, but uusally you can go below that minimum (but probably have a slightly lower APY - but still higher than a savings account). If you aren't dipping into your savings a lot every month, you should explore this option. Sure, .39% isn't a lot - but every little bit helps and when rates go back up, the gap between the savings and money market account will widen. Also with most banks, the more savings you have, the higher your APY.
Remember to always check the fees schedule when opening new accounts and whatnot. Some banks may charge a fee if you fall below a certain dollar amount. Some have restrictions. Sometimes the higher interest rate won't offset these fees - but every bank and credit union is different so take the couple minutes to read up on these things!