Op,
I assume you mean leave work and claim a top up on your partners earnings from tax credits, (working tax and child tax credits).
And I don't think you mean you intend to sign in 'the dole' / jobseekers .
The old/being phased out system of tax credits would allow you to do this, based on your partners income being under a certain thresh hold, you could apply for tax credits and receive them while he received his wage. But what you have to factor in is this system is being faced out quickly.. and replaced with universal credits. Also tax credits are usually based on the previous years earnings..
Most areas are live now for universal credits.
Meaning, that new claimants and people with a serious change in circumstance, are put straight into a universal credit claim, rather than applying for housing benefit with their council, and tax credits with DWP as it used to be.
You can check if you are in a live universal credit area online, but it is likely.
Be warned, universal credit is no game..
If you have a child over 1 you will be expected to look for work, but especially with a three year old. You will be made to sign an agreement, saying you will actively seek work, over 35hours. It will not matter what your partner works. They will monitor your online job searching and applications on the website they give you.
Universal credit is a hell hole.
You can be sanctioned for the slightest thing, and because it is a one monthly payment of all benefits, that can mean losing ALL monthly benefits. You will be forced back into work. Or you will go mad first.. one of the two.
You may know people who have managed to do what you are trying to, but they may have existing tax credit claims and not YET be over into universal. Which is hugely different.
I'm not sure about the partner moving out comment. If it is to claim benefits as a single parent.. not a good idea.
Plus, if you are in a live area for universal, you will be put on it anyway and forced into work because of your child's age..
Beat in mind universal payments are also less than tax credits were with the old system.
Inviting them into your life would be a lot More stressful than you anticipate, and I guarantee , you would regret it.
Hope this was helpful and Everything works out