Jenstar, be careful if you decide to do that. In general, employers tend to pay a month's wages instead of serving notice because once your helper knows she is being dismissed, there's always the chance that she may try to sabotage your household, or at the least, run up a lot of debts, knowing that she is leaving.
Not saying that's always the case but that's what happened to us. Our previous DH wasn't working out and I had decided to replace her. But we felt bad kicking her out immediately (she had worked for us for one year) and so even though I paid her the extra month's wages as notice, I let her stay on working for us (paid of course) until my new helper arrived. In fact she told me she was homesick as well, so I thought there was little risk as we were parting more or less "amicably".
Well after she left, we had months of phone calls from debt collectors - banks as well as phone companies (she managed to ring up a bill of almost $2000 in phone bills in 2 months!)