I've been living on a Macbook pro and doing my photography on it for many years. I haven't owned a desktop computer for 7-8 years.
So you can do it, but with some significant caveats.
I just upgraded my computer from a 2010 Macbook Pro 13" to a new 2013 Macbook Pro 15". The amount of processing capability is significantly different (geekbench value for the old computer: 2100. For the new one: almost 11,000). One big caveat is whether your 2009 Macbook is a smaller screen or a larger one: the smaller screen units are built around battery conservation over processing power, and I found the 2010 13" simply wasn't able to handle the kind of work I was pushing at it. The 15" (or in that era 17") Macbook pros were more powerful but you may find the limits on amount of RAM they can use and the processing power will limit how fast you can get things done. If you're using a modern camera with a larger megapixel count, this'll b a lot more noticeable.
You'll want a larger monitor. I found the 13" monitor too small to do serious work in Lightroom on the road, but okay for basic tasks (importing and ding deletion, for instance). I'm finding the 15" retina makes a big difference here, but when I'm at home, I'm plugged into a big monitor (in my case, a Dell 27" IPS. They're surprisingly reasonable in price). I do use a colormunki to calibrate my screens.
The bottom line to me is this: if that's a 2009 13" Macbook pro, you probably won't be happy; the computing power and RAM will be limited enough to hamper your work. A 15" or 17" Macbook may (or may not be) powerful enough. I think a 13" screen is too small, but is solvable by adding an external monitor for the home setup.
A lot also depends on your camera bodies; if you're working on 12 megapixel images it requires a lot less horsepower than 16 or 18 megapixels. If you're not doing video or timeplapse or HDR, it'll be more usable than if you are. You'll want to max the RAM on the thing (probably 8 gig) and ought to consider running Mavericks because it significantly improves RAM usage, even for Adobe apps that eat RAM alive.
I personally wouldn't use a 2009 era 13" macbook for photography work. I might use a 2009 era 15" macbook; it's performance capabilities would be right on the edge for normal Lightroom work, but I wouldn't consider it fast enough for handling video and I'd be arguing with it about how fast it was doing HDR and other kinds of enhanced processing.
That said, not knowing how old the desktop machine you're thinking of retiring it or its capabilities, it may still be an improvement over what you have. If it's from the same era, probably. If it's newer, I probably wouldn't step backwards to an older Mac system.