Whether you do it all at once or not, I'd tackle the most important aspects first.
One of the questions I ask clients is if they get a lot of repeat business. If the answer is "yes," I tell them to keep at least a bit of continuity between the old design and the new. Even if that's just a color scheme. You don't want the new design, however great it may be, to be too jarring. You want to create the feeling of, "This is the same business; they just have a cool new look."
In your case, I love the idea of your logo, but I would trim the amount of icons and clean up the presentation. That way it's different while still keeping some of the look and feel.
Whether or not you have repeat business is secondary to having the look match what you're selling. Some businesses make the mistake of having the pendulum swing way too far in the opposite direction when re-designing. I've seen an online toystore shift from being playful to overly corporate looking, and they lost a ton of sales. The playfulness that you have in your logo is very appropriate to what you sell. Just take that idea and sharpen it.
Good luck, Karen!