I believe you can make it work by taking a LOT of very light cuts. HOWEVER, a router table is a must-have. And it can't be one of those bench-top aluminium tables that sell for $100-$200. The hole in the top won't be big enough for your raised-panel bit. And you'll need a rail/stile set in addition to your raised panel bit. You're getting into some serious money for a couple of raised-panel doors if this is not going to be a continuing hobby.
Now, if woodworking is going to be something you continue to do, then you'll never regret the money you spend on a 3.25 HP router, even if you never make any more raised panel doors. You can get a Triton TRA001 for only about $50 more than the Milwaukee you're looking at. It's a little big for hand-held use, and you'll want smaller router too someday. But it will be the right tool for the job at hand.
“We should be careful to get out of an experience only the wisdom that is in it and stop there lest we be like the cat that sits down on a hot stove lid. She will never sit down on a hot stove lid again and that is well but also she will never sit down on a cold one anymore.” - Mark Twain