I work in the publishing industry (used to work in children's but don't any more) and yes, it is extremely competitive. That's no reason not to try (loads of people are professional writers of kid's books, why shouldn't you be one of them?) but you will need hard work and a fair dollop of luck.
My advice is:
You say you had an activity book in mind - this is going to be a hard pitch. Most activity books are part of a series and are often collaborative efforts from a team, rather than the work of a single author. Publishers who produce them in-house will already have a department to deal with that - perhaps you could look into joining that team?
You will need a USP and for your book to have a distinctive angle. You want to stand out and offer something no one else is.
Publishers prefer publishing authors who are offering a series rather than a one off, espec of activity books. Think about what the next book would be as well as this one.
Do a lot of research into what is already out there and who is publishing what.
Know EXACTLY where your book would slot in - the age range, the skills covered, the teaching method, etc. Who would be your main competition? Is there a gap that you have spotted that only your book can fill?
You will need to sell YOURSELF as well as your book - what can you offer that means you are the best possible person to write that book? Are you a teacher, have you studied child development, fostered many children, etc. Think about what you can bring to the process that will encourage publishers to sign you.
If you are planning to create the images, you will need a rock solid portfolio that really shows what you can do. It's great (but not essential) if some of this is professional commissions. If you don't have that at the moment, consider taking on freelance work.
Money-wise, that kind of is a tricky question - but it's generally less than people think. Two grand would be at the higher end of what a first time author could expect (in my experience, but it would depend on the publisher). The vast majority of authors in the UK have another job or other means of support - it's very hard to just live on the money your books make. That's not to say you might not become one of the big hitters - you might be the next Julia Donaldson or Lauren Child!
I have no idea what your book is like - I'm sure it's excellent - but one of the reasons the children's market is hard to get into is because (and I m not saying this is you) SO VERY MANY PEOPLE think they could just toss out a children's book. I have read an awful lot of half- thought out submissions from (often) new parents who a) look at Where's Spot and think "I could do that", b) think that making up stories for their toddler makes them JK Rowling and c) think that their personal experience of raising their own child is something THE WORLD NEEDS TO KNOW ABOUT. Approach it professionally, do you research and you'll already be head and shoulders above the vast majority of submissions, OP. Best of luck.