If your daughter can buy the house on her own, then Dan's advise is correct and you should contact a mortgage broker. If you are buying the house for her and you are already a home owner, then lenders will consider the house you are buying for your daughter an investment property and 20% down is common, some lenders are now requiring 25% down on investment properties.
Yes there is. Ther are programs available for first time home buyers with as little as 3% down. Ther are some government programs that offer downpayment assistance as well. You should have her talk to a godd mortgage broker about her options. If you would like the name os some, you can contact me.