For 15 V input, the IRF720 is somewhat oversized in terms of VGS (while the current rating might apply).
These days, all major semiconductor suppliers (e.g. TI, AD, OnSemi, NXP/nexperia etc.) offer DC/DC controllers with integrated MOSFET(s) for such applications, e.g. TI the TPS54320 or TPS65281 (both rated @ up to Vin = 17 V resp. 18 V, Iout = 3A).
Or an LM2576HV (60 V / 3 A).
Recent DC/DC converters come with a MOSFET replacing the free-wheeling diode, lowering the losses during free-wheeling.
You can use the IRS2184 MOSFET gate driver. This driver can drive both a high side and a low side MOSFETs in a half-bridge configuration. It also has an internal dead time of 400 ns to prevent shoot through.
If you do not want a half-bridge arrangement, you can use either the high side or the low side output only.
Note: If you maximum input voltage is 15V, you could safely use a MOSFET with a Vds rating of 50 V; this results in a cheaper device and lower gate charge.