Wow, big subject.
Basically there's so much variety to Europe, you know what you like and what you want to see. Have you been? What interests you?
I will say that southern Europe gets very busy and very hot in July and August. If you want to visit Greece, southern Italy, Spain, France, etc. plan to do that as soon as you arrive. June is really ideal for seeing Europe. Most European schools don't get out till July so you basically would have it all to yourselves for the first few weeks. The weather is good, everything's open and the crowds are yet to come!
That's especially true if you want to see "famous stuff". Go do the Eiffel Tower and the Vatican right away, if you want to include them. Standing in line for ages with a 4 year old is not fun. Experience speaking!
I would then recommend heading north, if that's where you want to go. Scandinavia? Germany? Baltic countries? Low countries? Your call.
If you want to do beaches, select carefully. I'm not a big fan of Spanish beaches but do your homework. Take your daughter to see the amazing places in the interior and Barcelona is probably the most kid-friendly city I've visited here. For beaches, you might want to go elsewhere...
Even then, you'll want to be sure to reserve and plan for July and August. It's not the best time in Europe to be spontaneous unfortunately. I love being spontaneous myself but please don't risk it with a child in tow. Seriously, there can be no room at the Inn.
She's a good age to go and you may find she's still free for a lot of perks.
I'm big into promoting train travel with children. Driving in Europe can be dodgy, the gas is expensive and in summer, it can be grim, hot and exasperating. The train is calm and you can get up and move around. The scenery is better and the network is great in Europe. There are passes but I can't tell you more. It can get complicated (by country, time frame, etc.) but it's usually budget-friendly to get around this way.
Low-budget companies are the new, hot thing here in Europe now. Ryan Air and Air Europe are the biggies but there are others. I would keep this in mind if you want to do a big leap, like go from Spain to England or over to St. Petersburg. It might cost less than taking an overnight train, depending on the train travel package you have. I took my kids to London last summer from Germany and it was cheaper than going by train. Also good if your train pass expires and you still want to hop around.
Happy planning!