(Does this doru mean doll or dollar? For the sake of simplicity, let me assume we are talking about a doll, because it's a very simple tangible noun.)
Can I assume that using 'Sukoshi' or 'Takusan' are preceded by 'Wa' particle?
No, you cannot. The particle choice depends on the context, what you want to focus in this particular sentence. The adverb takusan does not affect the particle choice. Let us remove that adverb for now and think about the difference between the following two sentences:
Dōru o motte imasu.
Dōru wa motte imasu.
Both sentences are grammatical. Although these are both translated into English as "I have dolls", in Japanese, you have to choose the correct particle depending on the context.
As you know, 持つ motsu is a transitive verb that basically takes an object marked with を. But when an object is topicalized, は replaces を. See this chart. So the first sentence is a "plain" version, and the second one is a version where the object, dōru, is marked as the topic of the sentence.
What does that mean? The は-version is used when dōru has been already mentioned in the conversation and you want to say something about it. You don't introduce something into the conversation using a topic marker.
A: (Do you have dolls? / We need some doll for the event tomorrow.)
B: Dōru wa (takusan) motte imasu.
The を-version is used to introduce dōru into the conversation for the first time. Typically this is true when you start some story with this sentence, or when you respond to a question where dōru itself is the answer.
A: (What's that in your hand? / What's your hobby?)
B: Dōru o (takusan) motte imasu.
Again, the adverb takusan is optional. It doesn't affect the particle choice. In case you didn't know about the function of は as the topic marker, please read: What's the difference between wa (は) and ga (が)?